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Short Book Reviews
Reviews 1996
Title MARKED POINT PROCESSES ON THE REAL LINE. THE DYNAMIC APPROACH. Author G. Last and A. Brandt. Publisher New York: Springer-Verlag, 1995, pp. xiv + 490, US$49.95. Contents:
1. Overview
2. Measurability concepts for stochastic processes, point and jump processes and random measures
3. Projections
4. The compensator: Definition and basic properties
5. The point process
6. The marked Poisson process
7. Continuous time Markov chains
8. Existence and uniqueness of point process distributions
9. Stochastic ordering
10. Absolute continuity
11. Filtering
APPENDIX 1: Monotone Class Theorems
APPENDIX 2: Kernels and Disintegration
APPENDIX 3: Conditional Probabilities and Conditional Distributions
APPENDIX 4: Lebesgue-Stieltjes Calculus
APPENDIX 5: Random Times and Hazard Measures
APPENDIX 6: Order Statistics
APPENDIX 7: Martingales
APPENDIX 8: Stochastic OrderingReadership: Researchers and graduate students in probability
A marked point process basically exhibits two random components: a stochastic point realization (localization) in space or time, together with a stochastic size (mark) effect. A typical example is given by moon craters, say, where besides the localization on the lunar surface, craters are further characterized by size variables (width and depth for instance). Recent applications include such diverse fields as reliability, medicine, physics and economics. The mathematical theory of point processes is strongly based on martingale theory through the notion of compensator. The authors give a comprehensive discussion of the relevant theory mainly using the martingale approach. Though most results are formulated in great generality, various special applications are also given. The resulting text is definitely demanding, offering the expert a comprehensive overview of the necessary theory.
Reviewer: Institute ETH-Zentrum Place Zürich, Switzerland Name P.A.L. Embrechts
Title ASPECTS AND APPLICATIONS OF THE RANDOM WALK. Author G.H. Weiss. Publisher Amsterdam: North-Holland, 1994, pp. xiv + 361, Dfl.115.00/US$88.50. Contents:
1. Introductory comments
2. The ubiquitous characteristic function
3. Asymptotics and the diffusion limit
4. Lattice walks
5. Boundaries and constraints
6. Multistate random walks
7. Selected applicationsReadership: Physical scientists, engineers and probabilists
This book, a substantive collection of concepts and applications, is one volume in a series entitled, "Random Materials and Processes", that is directed toward statistical physicists and engineers. The random walk is presented as the common stochastic process structure to a wide variety of models in polymer physics, crystallography, diffusion, reaction kinetics and biological migration. The author shows considerable knowledge of these diverse areas of application, so the reader receives a clear sense of the dynamic importance of probabilistic methods throughout science. The mathematical side of the presentation leans heavily toward the heuristic, and notation is biased toward the physicist, for example, ????? for expectation. Nevertheless, the book is recommended to the theoretically tolerant probabilist as an informative survey of the broad scope of interesting applications of the random walk being made today. On page 221, in the context of giving a heuristic derivation of the Donsker-Varadhan approximation, the author stresses that "The distinction between the inequality produced by our argument as opposed to an actual approximation ... is not sufficiently emphasized in the physics literature." There are numerous references to the broad literature at the end of each chapter. How-ever, there is no overall bibliography at the end of the book. The use of the reference style [M3] in the body of the text is not helpful, and the one page index is far too terse for a book of such scope.
Reviewer: Institute University of Washington Place Seattle, U.S.A. Name R. Pyke
Title RANDOM FIELDS ON A NETWORK. MODELING, STATISTICS, AND APPLICATIONS. Author X. Guyon. Translated by C. Ludeña. Publisher New York: Springer-Verlag, 1995, pp. xii + 255, DM.82.00/ÖS.598.60/Sw.fr.79.00. Contents:
1. Second-order stationary models on Zd
2. Gibbs and Markovian fields
3. Limit theorems and parametric estimation for fields
4. Estimation for second-order processes
5. Estimation of Gibbs fields
6. Stochastic algorithmsReadership: Students of spatial processes with a strong background in probability theory
This is a very welcome compendium of results on the theory of spatial processes on lattices, being especially strong on the contributions of the French school. The emphasis is on the precise statement of asymptotic results. Do not be misled by the subtitle; this is a book in Springer's series on 'Probability and its Applications', and all but one of the examples are synthetic ones reproduced from pioneering papers. A thorough knowledge of rigorous probability theory is assumed from the first page.
Its value as a reference text is diminished by the very brief index and rather incompletely specified (and inaccessible) references. But I know of no other book that covers most of the material, so perseverence is likely to be rewarded by the discovery of gems. G. Winkler's Image Analysis, Random Fields and Dynamic Monte Carlo Methods, [Short Book Reviews, Vol. 15, p.49.] is also mathematical, but has more introductory material and examples, and often covers complementary aspects of the subject.
Reviewer: Institute University of Oxford Place Oxford, U.K. Name B.D. Ripley
Title H? -OPTIMAL CONTROL AND RELATED MINIMAX DESIGN PROBLEMS- A DYNAMIC GAME APPROACH, 2nd edition. Author T. Basar and P. Bernhard. Publisher Boston: Birkhäuser, 1995, pp. xi + 411, DM.1118.00/ÖS.861.40/Sw.fr.98.00. Contents:
1. A general introduction to minimax (H?-optimal) designs
2. Basic elements of static and dynamic games
3. The discrete-time minimax design problems with perfect state measurements
4. Continuous-time systems with perfect state measurements
5. The continuous-time problem with imperfect-state measurements
6. The discrete-time problem with imperfect-state measurements
7. Minimax estimators and performance levels
8. Robustness to regular and singular perturbations
APPENDIX A: Conjugate Points and Existence of Value
APPENDIX B: Danskin's TheoremReadership: Control theorists
"H?" has become one of the cornerstones of modern control theory. The method can be described from different angles but one of the simplest is to see it as a procedure for minimizing a worst case scenario. Hence one of the natural ways to formulate this problem is as a dynamic game. This book is a second edition of this very well known text on H? theory. New topics include nonlinear systems, risk sensitive stochastic control, H? filtering and robustness issues. This topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with this important theoretical development in applied mathematics and control.
Reviewer: Institute University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title OBSERVATIONAL STUDIES. Author P.R. Rosenbaum. Publisher New York: Springer-Verlag, 1995, pp. xiii + 230, US$44.95 .
Contents:
1. Observational studies
2. Randomized experiments
3. Overt bias in observational studies
4. Sensitivity to hidden bias
5. Known effects
6. Multiple reference groups in case-referent studies
7. Multiple control groups
8. Coherence and focused hypotheses
9. Constructing matched sets and strata
10. Some strategic issuesReadership: Statisticians, epidemiologists, researchers
This is a fascinating book which combines elegant theory with good practical advice on applications, including in-depth discussion of many interesting examples from diverse fields. Fittingly the first sentence cites William G. Cochran and the spirit of his work pervades the book. Some researchers and statisticians use elaborate models in an attempt to control for bias in observational studies: this text emphasizes the virtues of simplicity, common sense and the use of sensitivity analyses to explore the possible effect of hidden variables. The mathematical level is variable-at times requiring some sophistication in probabilistic reasoning-and the exposition can be quite conceptually demanding. At times the book claims to do more than it actually does, for example the definition of "coherence" (Chapter 8) never really materializes. Not all epidemiologists will be as enthusiastic as Dr. Rosenbaum about the use of multiple control series. Each chapter ends with bibliographic notes and an index. The book would form an excellent basis for a seminar course on observational studies.
Reviewer: Institute University of Rochester Place Rochester, U.S.A. Name D. Oakes
Title STATISTICAL METHODS IN MEDICAL RESEARCH, 3rd edition. Author P. Armitage and G. Berry. Publisher Oxford: Blackwell Science, 1994, pp. xi + 620, US$69.95. Contents:
1. The scope of statistics
2. Probability
3. Sampling
4. Statistical inference
5. Regression and correlation
6. The planning of statistical investigations
7. Comparison of several groups
8. Further experimental designs
9. Further analysis of straight-line data
10. Multiple measurements
11. Data editing
12. Further analysis of categorical data
13. Distribution-free methods
14. Survival analysis
15. Sequential methods
16. Statistical methods in epidemiology
17. Biological assay
18. Statistical computationReadership: Medical researcher, statistician
Sixteen years separated the second edition of this compendium of biostatistical techniques from the original. This third edition came along "only" seven years later presumably because of the quickened pace of both development and use of statistical methods in biomedical science. There is a remarkable constancy of structure to the book-the chapter titles are basically the same in all three editions-testimony to the perspicacity of the first (in both senses) author, who recognized twenty-five years ago not only where the field was, but where it was going. Revisions in the new edit-ions modernize selected topics by inserting sections on current methods. For example, the third edition features an expanded treatment of survival data analysis, more on regression diagnostics, an introduction to k-group distribution-free tests. Rarely is a section deleted and most are untouched. Thus, the revisions exacerbate the original book's sole slight imperfection, a tendency to intermix easy and difficult techniques with no hint to the reader which is which, and to provide explanations inverse in length to the difficulty of the problem. The third edition is about ten percent longer than the second and true to the early intent to keep the mathematics accessible to those "with the ability to follow straight-forward formulae". In summary, this classical beauty has aged well.
Reviewer: Institute Fred Hutchinson Cancer Research Center Place Seattle, U.S.A. Name P. Feigl
Title STOCHASTIC MODELING OF SCIENTIFIC DATA. Author P. Guttorp. Publisher London: Chapman and Hall, 1995, pp. xii + 372, £29.95. Contents:
1. Introduction
2. Discrete time Markov chains
3. Continuous time Markov chains
4. Markov random fields
5. Point processes
6. Brownian motion and diffusion
APPENDIX A: Some Statistical Theory
APPENDIX B: Some Theory of Partial Differential EquationsReadership: Researchers, lecturers and students studying applied probability and stochastic processes
Though the book's title could have been "Applied Stochastic Processes", the present one makes it very clear that the aim is much broader than the usual textbook on the subject. Based on numerous sets of data, obtainable via ftp, the author concentrates on the real questions asked in practice. Theory is presented in a very informative way as the data analysis proceeds. The result is a wonderful text where probability and statistics enter jointly in the realm of stochastic modeling. Especially, the various excursions to statistical estimation and testing offer an import-ant added value. From the table of contents, it is clear that the main emphasis lies on Markovian models. Both on the undergraduate as well as graduate level, a lot of interesting teaching material is contained in this superb book. I highly recommend it.
Reviewer: Institute ETH-Zürich, Place Zürich, Switzerland Name P.A.L. Embrechts
Title AIDS CLINICAL TRIALS. GUIDELINES FOR DESIGN AND ANALYSIS. Author D.M. Finkelstein and D.A. Schoenfeld(Eds.). Publisher New York: Wiley, 1995, pp. xiv + 468, £40.00. Contents:
1. Introduction, by D.M. Finkelstein and D.A. Schoenfeld
2. The natural history of HIV infection: Implications for clinical trials, by D.J. Cotton
3. The new drug evaluation process: FDA perspective, by S.L. Keder, R.T. O'Neill and P. Beninger
4. The new drug evaluation process: Industry perspective, by A.P. Cross and L.M. Dunkle
5. Protocol development, by A.H. Korzun and K. Chaloner
6. Data issues in AIDS clinical trials, by K. Stanley
7. Current methods and future trends in the design and analysis of Phase I and Phase I/II clinical trials in AIDS, by Y.C. Bassiakos, M.L. Feldstein, T. Fenton and H. Geheb
8. Selection of endpoints for assessment of treatment efficacy in an AIDS trial, by D.A. Amato
9. The uses of CD4 lymphocyte count to evaluate therapy for HIV disease, by V. De Gruttola, R. Gelman and S.W. Lagakos
10. Sample size calculations for failure time data, by P.L. Williams
11. The design and analysis of equivalence trials, by D.A. Amato
12. Interim monitoring of clinical trials, by M.D. Hughes and S.J. Pocock
13. Behavioural science and the design and conduct of randomized AIDS trials, by K. Taylor
14. Compliance in AIDS clinical trials, by J.E. Buring and C.H. Hennekens
15. Quality-of-life considerations in AIDS clinical trials, by M.A. Testa and W.R. Lenderking
16. Issues in analysis of AIDS clinical trials, by D.M. Finkelstein and S.B. Green
17. Issues in the testing of drug combination, by D.A. Schoenfeld
18. Issues in the conduct of clinical trials for HIV- infected children, by J.C. Lindsey, R.E. McKinney, Jr. and K.J. Propert
19. Clinical trials to reduce the risk of maternal- infant transmission of HIV infection, by R.D. Gelber, J.C. Lindsey and S. MaWhinney
20. Obstetrical and gynaecological issues in AIDS clinical trials, by C. Spino and P. Stralton
21. Prophylactic HIV vaccine trials, by W.N. Rida and D.N. Lawrence
22. Large sample trials of HIV therapies, by M.A. Foulkes and S.S. Ellenberg
23. Economic analysis and AIDS clinical research, by A.A. Stinnett and A.D. Paltiel
24. Use of observational data for evaluating AIDS therapies, by M.H. Gail
25. Use of cohort studies for evaluating AIDS therapies, by A. Murloz and D.R. HooverReadership: Medical researchers, biostatisticians and epidemiologists
There are forty-four contributors to this outstanding volume, dedicated to the memory of David Byar. It is an indispensable reference for planning, designing, conducting and analyzing AIDS trials but it will inspire researchers involved in the study of other diseases too. The statistical problems arising from AIDS clinical trials are unique because of the history of the disease, the very rapid changes in its treatment and the active role of the patients' community. These characteristics are clearly presented in the first four chapters. Chapters 5 to 17 are the core of the volume, where the issues of planning and designing (and con-ducting) a trial are thoroughly reviewed. The ethical considerations which arise when studying HIV-infected pregnant women and children are addressed in the latter part of the volume which ends with two overviews of epidemiological data. Most chapters have a summary which allows one to go intelligently through the enormous amount of information held in the volume. The only criticism, if at all appropriate, is the absence of any reference to non-western countries.
Reviewer: Institute London School of Hygiene and Tropical Medicine Place London, U.K. Name B.L. De Stavola
Title ECOLOGY OF INFECTIOUS DISEASES IN NATURAL POPULATIONS. Author B.T. Grenfell and A.P. Dobson (Eds.). Publisher Cambridge University Press, 1995, pp. xii + 521, £35.00/US$59.95. Contents:
Introduction
PART I : Broad Patterns and Processes
1. Impact of infectious diseases on wild animal populations: A review, by F.M.D. Gulland
2. Microparasites: Observed patterns, by A.P. Dobson and P.J. Hudson
3. Mathematical models for microparasites of wildlife, by J.A.P. Heesterbeek and M.G. Roberts
4. Microparasite group report, by C. Dye (Ed.)
5. Macroparasites: Observed patterns, by P.J. Hudson and A.P. Dobson
6. Mathematical models for macroparasites of wildlife, by M.G. Roberts, G. Smith and B.T. Grenfell
7. Macroparasite group report, by G. Smith (Ed.)
8. Critical evaluation of wildlife disease models, by N.D. Barlow
PART II : Pathogens, Insects and Plants
9. Non-linearities in the dynamics of indirectly- transmitted infections (or, does having a vector make a difference?), by C. Dye and B.G. Williams
10. Model frameworks for plant-pathogen interactions, by J. Swinton and R.M. Anderson
11. The dynamics of insect-pathogen interactions, by C.J. Briggs, R.S. Hails, N.D. Barlow and H.C.J. Godfray
PART III: Impact of Ecological and Genetic Heterogeneity
12. Environmental influences on host immunity, by S. Lloyd
13. Modelling the immuno-epidemiology of macroparasites in wildlife host populations, by B.T. Grenfell, K. Dietz and M.G. Roberts
14. Spatial dynamics of parasitism, by D. Mollison and S.A. Levin
15. Spatial dynamics group report, by B.M. Bolker (Ed.)
16. Genetic diversity in host-parasite interactions, by C.M. Lively and V. Apanius
17. Genetics and evolution of infectious diseases in natural populations group report, by A.P. Read (Ed.)
18. Beyond host-pathogen dynamics, by M. Begon and R.G. Bowers
19. Glossary, by C. Watt, A.P. Dobson and B.T. GrenfellReadership: Epidemiologists, biomathematicians, ecologists, zoologists, plant pathologists, veterinarians, wildlife managers
This volume is the outcome of a workshop convened in March 1993 by the Isaac Newton Institute programme on epidemic models. It presents the current understanding of the quantitative ecology and epidemiology of infectious diseases in naturally-fluctuating animal and plant host populations. A group of international and interdisciplinary experts have writ-ten background chapters reviewing theoretical and empirical research into the dynamics of infections in natural populations. Interspersed among the background chapters are the reports of four specialist groups who met during the workshop; these deal with the population biology of microparasites, the population biology of macroparasites, the spatial dynamics of parasitism, and with the genetic and evolutionary issues. Both kinds of chapter include useful bibliographies. There is a helpful glossary; unfortunately there is no index.
A dominating theme concerns the balance of new theory and new empirical work that would best advance the subject. Further empirical research is thought necessary concerning the diversity of host-parasite interactions and the manipulation of such inter-actions. New theoretical tools are also wanted, for example for the study of the dynamics of immunity, spatial infection processes and host-parasite population genetics.
Reviewer: Institute St. Andrews University, Place St. Andrews, U.K. Name A.W. Kemp
Title EPIDEMIOLOGICAL RESEARCH METHODS. Author D.McNeil. Publisher New York: Wiley, 1996, pp. x + 305, £19.99. Contents:
1. Epidemiological research
2. Statistical methods I
3. Statistical methods II
4. Mantel-Haenzel methods
5. Logistic regression I
6. Logistic regression II
7. Survival analysis
8. Matching
9. Sample sizeReadership: Students, teachers and medical researchers
This book on epidemiological methods is de-signed for final year undergraduate or masters level students in statistics and for medical scientists. Its goal is to combine material on observational and experimental studies in a single source and it uses an inductive approach based on examples. The topics and methods discussed represent a good choice for the in-tended readership. There is a need for such a book and I think the book will prove useful.
The author has successfully tried to keep the mathematical level of the book down and takes care to demonstrate clearly even relatively simple algebraic manipulations which are necessary to a development. The reader is therefore introduced to some important methods without excessive technical baggage. This is particularly helpful to the medical scientists but, from the vantage point of the statistics student, some peculiarities arise. In the discussion of two sample t-tests, the equal variance assumption is mentioned but it is suggested that it be assessed by box-plots with no mention of a F-test. The invariance of the odds ratio in 2 X 2 tables under retrospective and prospective sampling is explained for example but I did not find even a reference to the comparable invariance for logistic regression although logistic regression for the analysis of case-control studies is a major topic in the book. The discussion of matched logistic models proceeds without ever introducing pair-specific parameters explicitly. Some augmentation of the material might well be necessary therefore if the book is used as a text for statistics students.
Throughout the book, the numerical results presented are those seen in standard packages and this is an attractive approach. Uncritical reliance on this approach did mean, however, that R-squared values were presented and discussed for logistic regressions with-out any attention being given to the suitability of the calculation for binary outcome variables.
This book covers a lot of material (somewhat more on methods for observational epidemiological studies than for clinical trials), presents many examples and the writing is clear and direct. Overall the author does what he intended to do and I think the book can be a valuable teaching resource.
Reviewer: Institute University College London Place London, U.K. Name V.T. Farewell
Title INTERPRETING EVIDENCE. Evaluating Forensic Science in the Courtroom. Author B. Robertson and G.A. Vignaux. Publisher Chichester, U.K.: Wiley, 1995, pp. xxi + 240, £24.95. Contents:
1. Introduction
2. Interpreting scientific evidence
3. The alternative hypothesis
4. Explaining the strength of the evidence
5. The case as a whole
6. Errors of thinking
7. Classical statistics and database matching
8. Transfer evidence
9. Blood and DNA evidence
10. Other scientific evidence
11. Implications for the legal system
12. ConclusionReadership: Lawyers, legal scholars, forensic scientists
The central tenet of the book is that scientific evidence should be quantified, and presented at court, in the form of likelihood ratios. The authors argue that many perceived and actual problems with scientific evidence result from its presentation in other forms, including probability statements akin to p-values. Further, a focus on the likelihood ratio necessitates consideration of the questions which are actually central to the correct interpretation of the evidence. Indeed, one of the advantages of a "Bayesian" approach in the trial context is that it seems very natural - the authors repeatedly claim that it is a matter of simple logic - at least to those (lawyers, judges, scientists) whose minds have not been closed by a surfeit of inappropriate statistical education. Statisticians and evidence scholars may find some aspects of the book disappointingly simplistic. Discussion of some of the difficult practical and conceptual issues which arise in this, or other, approaches, is limited, as is the treatment of some specific forms of evidence. The book should not be criticized on these grounds. It is aimed, as an introductory text, at lawyers and forensic scientists. This aim is laudable and the book succeeds in its aim. It is clearly written and enlivened by interesting, real, examples. What's more, the case the authors, and others, have made for the proper interpretation of scientific evidence is compelling.
Reviewer: Institute University of Chicago, Place Chicago, U.S.A. Name P.J. Donnelly
Title SEEING THROUGH STATISTICS. Author J.M. Utts. Publisher Belmont, California: Duxbury, 1996, pp. xvi + 464. Contents:
PART I : Finding Data in Life
1. The benefits and risks of using statistics
2. Reading the news
3. Measurements, mistakes and misunderstandings
4. How to get a good sample
5. Experiments and observational studies
6. Getting the big picture
PART II : Finding Life in Data
7. Summarizing and displaying measurement data
8. Bell-shaped curves and other shapes
9. Plots, graphs and pictures
10. Relationships between measurement variables
11. Relationships can be deceiving
12. Relationships between categorical variables
13. Reading the economic news
14. Understanding and reporting trends over time
PART III: Understanding Uncertainty in Life
15. Understanding probability
16. Possible futures: What to expect in the long run
17. Psychological influences on personal probability
18. When intuition differs from surveys and experiments
PART IV : Making Judgements from Surveys and Experiments
19. The diversity of samples from the same population
20. Estimating proportions with confidence
21. The role of confidence intervals in research
22. Rejecting chance - testing hypotheses in research
23. Hypothesis testing - examples and case studies
24. Significance, importance and undetected differences
25. Meta-analysis: Resolving inconsistencies across studies
26. Putting what you have learned to the testReadership: General
Commercial organizations, political factions, pressure groups, advertisers, journalists and the like are well aware of the credibility and impact of apparently independently conducted studies, surveys, experiments, etc. which present findings that happen to further the interests of those bodies. How is the public to develop a healthy scepticism of such reports? Some headway would be made if Part I of this book were made compulsory reading at high-schools, tertiary institutions and for all journalists. A set of key components that every report of a study or survey should include, are given early on in the book and these are regularly referred to throughout whenever new studies are introduced, throwing into relief any short-comings of the study. The book is pitched at a level readable by a wide audience and based in large measure on case studies. The text is never dreary, it carries the reader along from one interesting case study to another. It is clear that considerable effort went into the tracking down of stimulating sets if data. Parts 2, 3, and 4 introduce the more standard topics one would find in an introductory statistics course but again, very well motivated and requiring little or no mathematical knowledge. Excellent examples are included.
Reviewer: Institute Macquarie University Place Sydney, Australia Name J.R. Leslie
Title A CASEBOOK FOR A FIRST COURSE IN STATISTICS AND DATA ANALYSIS. Author S. Chatterjee, M.S. Handcock and J.S. Siminoff. Publisher New York: Wiley, 1995, pp. xi + 314 + disk, £19.95. Contents (60 cases arranged under the following headings):
1. Data analysis
2. Applied probability
3. Statistical inference
4. Analysis involving regressionReadership: Teachers and students of statistics
Designed to supplement traditional course material, the book covers a wide variety of application areas, most being U.S. based. The cases are distinguished in a second table of contents as F indicating a full analysis is presented, G a guide to the analysis is presented, thirteen cases; and O the analysis is open to the reader, nineteen cases. Every case contains a list of topics covered, some key statistical words, the names of the relevant data files, and background material on the application area including the questions that were, or might have been, of interest to the original researcher. Statistical terminology is defined as it appears.
The data files are on a PC-only formatted disk included with the book. The files are publicly avail-able over the world wide web in a variety of formats.
I have some reservations in recommending the casebook for its intended student use. The book focuses on the illustration of methods of analysis and pays too little attention to how the data came to be; at least half of the statistical story is missing. This point cannot be over-emphasized for the student. For many cases this information is absent; for others the data cannot address the primary questions of the re-search. Consequently some of the cases and questions posed seem artificial.
Despite its shortcomings, the careful instructor could make very good use of the book and should consider it a welcome instructional resource.
Reviewer: Institute University of Waterloo, Place Waterloo, Canada Name R.W. Oldford
Title CASE STUDIES IN BAYESIAN STATISTICS, Volume II. Author C. Gatsonis, J.S. Hodges, R.E. Kass and N.D. Singpurwalla (Eds.). Publisher New York: Springer-Verlag, pp. v + 364. Contents:
Invited Papers (with discussions)
1. A Bayesian model for organ blood flow measurement with colored microspheres, by E.N. Brown and A. Sapirstein
2. Elicitation, monitoring and analysis for an AIDS clinical trial, by B.P. Carlin, K.M. Chaloner, T.A. Louis and F.S. Rhame
3. Accurate restoration of DNA sequences, by G.A. Churchill
4. Analysis and reconstruction of medical images using prior information, by V. Johnson, J. Bohwser, R. Jaszczak and T. Turkington
Contributed Papers
5. Combining information from multiple sources in the analysis of a non-equivalent control group design, by T.R. Bolin, R.M. Elashoff, K.-M. Leung, R. Nisenbaum, R. Bastani, K. Nasseri and A. Maxwell
6. Road closure: Combining data and expert opinion, by G. Blattenberger and R. Fowles
7. Optimal design for heart defribillators, by M. Clyde, P. Muller and G. Parmigiani
8. Longitudinal care patterns for disabled elders: A Bayesian analysis of missing data, by S.L. Crawford, S.L. Tennstedt and J.B. McKinlay
9. Bayesian inference for the mean of a stratified population when there are order restrictions, by B. Nandram and J. Sedransk
10. Hierarchical modelling of consumer heterogeneity: An application to target marketing, by P.E. Rossi, R.E. McCulloch and G.M. AllenbyReadership: Statisticians with an interest in serious applications
The papers collected in this volume were presented and discussed at the second of a biannual series of workshops which are held at Carnegie Mellon University, this one occurring October 9-11, 1993. On this occasion biomedical applications were focussed upon. Each of the four major invited papers have two discussants and a reply, and the six contributed papers were selected from those presented at the workshop. The papers and accompanying discussions are very interesting from both a scientific and a statistical view-point. The substantial length of the invited articles allows the opportunity for a full description of the relevant science and the development of, often very complex, models using state-of-the-art Bayesian techniques. It is particularly satisfying to see the careful incorporation of relevant prior information. Volume 1 was reviewed in Short Book Reviews, Vol. 14, p.2..
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name J. Wakefield
Title STATISTICAL TESTS. An Introduction with MINITAB Commentary. Author G.P. Beaumont and J.D.Knowles. Publisher London: Prentice Hall, 1996, pp. ix + 285, £16.95. Contents:
1. Preliminaries
2. Data
3. Estimation
4. Tests of hypotheses
5. Tests related to the binomial distribution
6. Tests related to the hypergeometric distribution
7. Rank correlation coefficients
8. Distribution-free tests for many samples
9. Theory of hypothesis testingReadership: Students and teachers of introductory courses
A brief review of basic probability and standard distributions is followed by chapters on point estimation, interval estimation and hypothesis testing. These contain a good blend of simple theory and methodology. Most but not all of the examples are based upon normal theory assumptions and concern one sample or two samples. Brief mention is made of one-way analysis of means. Then follow four chapters on distribution-free methods which include the sign test, Wilcoxon rank sum tests, runs test, rank correlation, Mood, Kruskal-Wallis and Friedman's tests. The first eight chapters contain numerical examples and exercises using MINITAB (release 8). The reader is assumed to be able to enter data into MINITAB but other MINITAB commands are explained when required. The final chapter, intended as a basis for the methods presented earlier, is devoted to a formal discussion of hypothesis testing based upon Neyman-Pearson theory. More cross-references to those methods would have provided closer links with earlier chapters.
Reviewer: Institute _________________ Place Harpenden, U.K. Name E.J. Snell
Title PRACTICAL BIOSTATISTICAL METHODS. Author S. Selvin. Publisher Duxbury Press, 1995, pp. xv + 503. Contents:
1. General concepts
2. Simple linear regression
3. Linear regression with two independent variables
4. Multivariable regression
5. Analysis of covariance
6. Linear discriminant analysis
7. Principal components
8. Contingency table analysis
9. Log-linear models
10. Logistic regression analysis
11. Survival data analysis
12. Poisson regression analysisReadership: Undergraduate statistics/ biostatistics students
Many of us will have experienced students' hostility and impatience with any rigorous, or half-rigorous, development of statistical methodology. One cannot but have sympathy with them given that for most universities, only a small minority of statistics graduates will ever need to bother with the theoretical underpinnings of the more sophisticated statistical procedures. For many statistics graduates their primary needs are to be able to identify an appropriate statistical technique, to get their data into some package and to interpret the output. This text fulfils such requirements whilst avoiding the cookbook label. It steers a carefully negotiated path, providing just enough of the theory to offer, via broad brush strokes, some rationale for these widely used and important methods. Explanations are clear and a good range of examples is used including a major set of data that is analyzed throughout; a disc with the sets of data is provided. The relatively inexpensive but powerful package STATA is used for the analyses. Although the book has been pitched at second-year undergraduates who have done an introductory statistics course it will
serve as a useful reference for more advanced courses in these topics. Students who are distracted and/or intimidated by mathematical arguments will find the treatment of these topics most accessible.
Reviewer: Institute Macquarie University Place Sydney, Australia Name J.R. Leslie
Title HANDBOOK OF THE NORMAL DISTRIBUTION, 2nd edition, revised. Author J.K. Patel and C.B. Read. Publisher New York: Dekker, 1996, pp. ix + 431, US$135.00. Contents:
1. Genesis: a historical background
2. Basic properties
3. Expansions and algorithms
4. Characterizations
5. Sampling distributions
6. Limit theorems and expansions
7. Normal approximations to distributions
8. Order statistics from normal samples
9. The bivariate normal distribution
10. Bivariate normal sampling distributions
11. Point estimation
12. Statistical intervalsReadership: Statisticians, research workers, postgraduates and advanced undergraduates
The second edition of this book is very welcome as the first edition (1982) is still widely used but has become out-of-date [Short Book Reviews, Vol. 2, p.15].
The previous Chapters 1 to 8 now contain a lot of new material and references. Chapter 9, on Wiener and Gaussian processes, has been omitted and its material is not absorbed elsewhere. Chapter 10 is now Chapter 9. The new Chapter 10 is on bivariate normal sampling distributions, with emphasis on the sample correlation coefficient. The two other new chapters collate useful information on estimation procedures.
The expansion is greater than a page count would suggest because there is now more material per page. The pages do not look crowded however; the new fonts and typography are a great improvement on the previous typewritten text.
The failure to reference Johnson, Kotz and Balakrishnan (1994, 1995) Continuous Univariate Distributions Volume 1 [Short Book Reviews, Vol. 15, p.25] and Volume 2 [Short Book Reviews, Vol. 15, p.43] is unfortunate. Also I regret the low coverage of pseudo-random normal variate generation, compared with that on expansions and approximations. Nevertheless, an enormous amount of material is packed into this single volume. The new edition ought to be on the shelves wherever statisticians are located.
Reviewer: Institute St. Andrews University Place St. Andrews, U.K. Name A.W. Kemp
Title THEORY OF STATISTICS. Author M.J. Schervish. Publisher New York: Springer-Verlag, 1995, pp. xvi + 702, US$59.95. Contents:
1. Probability models
2. Sufficient statistics
3. Decision theory
4. Hypothesis testing
5. Estimation
6. Equivariance
7. Large sample theory
8. Hierarchical models
9. Sequential analysis
APPENDIX A: Measure and Integration Theory
APPENDIX B: Probability Theory
APPENDIX C: Mathematical Theorems Not Proven Here
APPENDIX D: Summary of DistributionsReadership: Graduate students and their teachers, mathematical statisticians
If you are on the lookout for an advanced textbook on the theory of statistics that is mathematically rigorous, but not excessively difficult, then this is the book for you. An ideology is not imposed, and both the frequentist and Bayesian approaches to mathematical statistics are covered. The book grew out of lectures on estimation, testing and large sample theory given to second-year graduate mathematicians working towards a Ph.D. in statistics. Sections can be found on topics that have been introduced to mainstream statistics only in recent years. These include the bootstrap, successive substitution sampling, for ex-ample, Gibbs, which is the basis of Markov chain Monte-Carlo methods, and Bayesian robustness. Sections which rely on martingale theory are starred, and proofs which involve measure theory arguments are not left out.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name R. Coleman
Title INFERENCE NON PARAMETRIQUE. Les Statistiques de Rangs. Author Edité par J.-J. Droesbeke et J. Fine. Publisher Editions de l'Université de Bruxelles; Paris: Editions Ellipses, 1996, pp. 304, B.Fr.1,500. Table des matières:
1. Une approche historique des statistiques de rangs
2. Tests de rangs: définitions et exemples simples
3. Tests sans biais, tests de permutation, tests invariants, tests de rangs
4. Eléments de la théorie asymptotique des expériences statistiques
5. Statistiques de rangs linéaires: normalité asymptotique et théorèmes de projection de Hájek
6. Tests de rangs et tests de rangs signés pour le modèle linéaire général et les modèles autorégressifs
7. R-estimateurs dans le modèle linéaire général
8. Méthodes non paramétriques: applications en marketingPublic visé: Statisticiens, chercheurs, étudiants et chargés de cours des cycles supérieurs en méthodes non paramétriques, spécialistes des statistiques de rangs
Ce livre est un recueil des textes des conférences données dans le cadre des sixièmes Journées d'Etudes en Statistique organisées périodiquement par l'Association pour la Statistique et ses Utilisations et consacrées à l'inférence non paramétrique à l'aide des statistiques de rangs. Il couvre l'essentiel de la théorie sous-jacente à l'estimation et aux tests d'hypothèses basée sur les rangs et issue principale-ment de travaux de pionniers de Hájek et de LeCam. Le premier chapitre est consacré à l'histoire des statistiques de rangs et fait remonter les premiers balbutiements d'une approche non paramétrique aux travaux quasi métaphysiques d'Arbuthnott (1667-1735) sur la disparité entre les naissances masculines et féminines à Londres entre 1629 et 1710. Le huitième et dernier chapitre présente des applications et marketing où l'utilisation de données ordinales est fréquente. Les chapitres médians sont d'un niveau mathématique plus avancé. L'approche par les bruits blancs utilisée au
Chapitre 3 permet de bien unifier les différents types de modèles que l'on retrouve dans la littérature. On peut cependant déplorer qu'à quelques exceptions près, les théorèmes et propositions soient énoncés sans esquisse de démonstration. Malgré la diversité des auteurs, un effort semble avoir été fait dans le but d'unifier la notation tout au long du livre. Dans l'ensemble, il s'agit d'un livre très bien écrit qui pourrait servir de manuel de base pour un séminaire de recherche en méthodes non paramétriques basées sur les rangs.
Reviewer: Institute Université de Sherbrooke Place Sherbrooke, Canada Name E. Monga
Title RANDOMIZATION TESTS, 3rd edition revised and expanded. Author E.S. Edgington. Publisher New York: Dekker, 1995, pp. xxii + 408. Contents:
1. Introduction
2. Random assignment
3. Calculating significance values
4. One-way analysis of variance and the independent t test
5. Repeated-measures analysis of variance and the correlated t test
6. Factorial experimental designs
7. Randomized block designs
8. Multivariate designs
9. Correlation
10. Trend tests
11. Matching and proximity experiments
12. Single-subject randomization tests
13. Tests of quantitative laws
14. Tests of direction and magnitude of effect
15. Theory
16. General guidelinesReadership: Researchers interested in statistical methodology who desire to know about the"half-hidden" assumptions behind the usual statistical tests and what to do if not satisfied.
The subject of randomization tests is quite strange to the average statistician who relies on random sampling and the usual tables of t, F, chi-square, normal, etc. to conduct tests of null hypotheses. In randomization tests we cannot assume random sampling and we have to rely on permutation and randomization tests, usually without any tables prepared in advance. The Type 1 error is there but it is difficult to find any analogue of power. The limitations of the randomization method are not very clear. For example, can you rank three or more treatments and assign a significance level to the result? Some questions I would like to see answered are: 1. What areas of this field need more research? 2. How is this subject related to other modern methods of re-using data, like bootstrap etc.?
The use of very small sizes at the beginning of the book may be good pedagogy but gives the impression that you can draw valid conclusions with small samples of size four. There is a tremendous literature on randomized tests. This book serves an important purpose in describing the breadth of the subject, its literature and its history and usefulness. It is not just a subject for psychology or sociology experiments; it is useful whenever the assumption of random sampling is questionable. One could argue that there ought to be a special course on this topic in any respectable statistical curriculum.
The author makes it clear in his preface that the third revised edition has new chapters and revised
chapters that justify a new edition. The book now has sixteen chapters, Chapter 13 on tests of quantitative laws and Chapter 14 on tests of direction and magnitude of effect being entirely new. Both of these deal with tests of null hypotheses. The case of ordering three treatments would be a nice example to get away from the null hypothesis, but there is a randomization test for that with a prescribed significance level. The first edition was reviewed in Short Book Reviews, Vol. 0, p.2.
Reviewer: Institute University of California Place Santa Barbara, U.S.A. Name M. Sobel
Title FACET THEORY: FORM AND CONTENT. Author I. Borg and S. Shye. Publisher Thousand Oaks: Sage, 1995 pp. xiv + 194. Contents:
1. An introductory example
2. Basic elements of facet theory
3. Observations
4. Definitional systems
5. Mapping sentences
6. Common range
7. Items
8. General principles of correspondence of design and data
9. Bivariate regression hypotheses
10. Hypotheses for structuples
11. Hypotheses for similarity structures
12. Some concluding comments on FTReadership: Social and behaviourial science students or researchers with either little or moderate familiarity with facet theory
The nearest the authors come to defining a facet in this book is to quote L. Gutman: 'By a facet we shall mean a set that is a component of a Cartesian product.' No standard term for this appears in the mathematical or other literature. Experience shows the need for such a term, to distinguish the idea involved from related but often radically different concepts denoted by "dimension", "factor", "element", etc.' So clearly the concept is related to an aspect, characteristic, or variable describing a situation, though the precise differences and relationships are never made clear. The observed set of facets is regarded as a sample from a larger, possibly infinite collection. Facet Theory is then concerned with sampling the facets to be observed and with making inferences from the ob-served sample to the entire universe of potential facets. It is not a particular statistical technique, but makes use of a variety of such techniques to make its inferences. For a one paragraph description of facet theory, see the review of Introduction to Facet Theory, S. Shye, D. Elizur and M. Hoffman [Short Book Reviews, Vol. 15, p.7]. This book is essentially an outline of facet theory and how to use it. The latter part of the book contains illustrations, embedded in the text, but I think it would have been improved by a set of explicit case studies. The book is aimed at social and behaviourial scientists and is more likely to appeal to them than to statisticians.
Reviewer: Institute The Open University Place Milton Keynes, U.K. Name D.J. Hand
Title CYCLIC AND COMPUTER GENERATED DESIGNS, 2nd edition. Author J.A. John and E.R. Williams. Publisher London: Chapman and Hall, 1995, pp. xii + 255, ,30.00. Contents:
1. Block designs
2. Efficiency factors
3. Cyclic designs
4. Resolvable block designs
5. Row-column designs
6. Resolvable row-column designs
7. Recovery of inter-block information
8. Factorial experiments: Single and fractional replication
9. Factorial experiments: Multiple replication
APPENDIX: Some matrix resultsReadership: Graduate students, researchers, statisticians
This is a revised and extended version of the book Cyclic Designs by J.A. John [Short Book Reviews, Vol. 7, p.28]. It has undergone substantial reorganization and includes much material developed since the first edition was prepared. This includes material on row-column designs, computer generation of both block and row-column designs and a section on neighbour analysis of field trials. The book concentrates on design, rather than analysis, with only two numerical examples given. I found very few misprints, but the page numbers in the index are slightly off from Chapter 6 onwards. The later chapters rely heavily on a sound knowledge of matrix algebra. The book assumes a basic knowledge of the field and will be a useful addition for post graduate students and researchers in the area of experimental design.
Reviewer: Institute University of Adelaide Place Adelaide, Australia Name R.G. Jarrett
Title RESPONSE SURFACE METHODOLOGY: Process and Product Optimization Using Designed Experiments Author R.H. Myers and D.C. Montgomery. Publisher New York: Wiley, 1995, pp. xiv + 700, £45.00. Contents:
1. Introduction
2. Building empirical models
3. Two-level factorial designs
4. Two-level fractional factorial designs
5. Process improvement with steepest ascent
6. The analysis of response surfaces
7. Experimental designs for fitting response surfaces-I
8. Experimental designs for fitting response surfaces-II
9. Miscellaneous response surface topics
10. Response surface methods and Taguchi's robust parameter design
11. Experiments with mixtures
12. Other mixture design and analysis techniques
13. Continuous process improvement with evolutionary operation
APPENDIX 1. Variable Selection and Model Building in Regression
APPENDIX 2. Multicollinearity and Biased Estimation in Regression
APPENDIX 3. Robust Regression
APPENDIX 4. Some Mathematical Insights into Ridge Analysis
APPENDIX 5. Moment Matrix of a Rotatable Design
APPENDIX 6. Rotatability of a Second-Order Equiradial Design
APPENDIX 7. Relationship Between D-Optimality and the Volume of a Joint Confidence Ellipsoid on â
APPENDIX 8. Relationship Between Maximum Prediction Variance in a Region and the Number of Parameters
APPENDIX 9. The Development of Equation (8.21)
APPENDIX 10. Determination of Data Augmentation ResultReadership: Quality engineers and scientists, chemical engineers, statisticians
This book gives a thorough and very clear description of today's most important techniques for product and process optimization. There are not many mathematical proofs but the most important aspects of response surface methodology are presented in detail and in a very convincing manner. Through a lot of real-world and constructed examples, the authors present practical ways for product and process optimization. The rich graphical material is very useful for the clarity of the text. The examples are developed by widely used software such as SAS and Design Expert. There are a lot of exercises at the end of each chapter.
Many practical details make process and product optimization an art, not simply a mathematical problem. The authors provide a valuable guidance to the best choice of product parameters or process conditions.
Reviewer: Institute University of Chemical Technology and Metallurgy Place Sofia, Bulgaria Name I.N. Vuchkov
Title DESIGN AND ANALYSIS OF EXPERIMENTS FOR STATISTICAL SELECTION. SCREENING AND MULTIPLE COMPARISONS. Author R.E. Bechhofer, T.J. Santner and D.M. Goldsman. Publisher New York: Wiley, 1995, pp. xii + 325, ,45.00. Contents:
1. The rationale of selection, screening and multiple comparisons
2. Selecting the best treatment in a single-factor normal response
3. Selecting a subset containing the best treatment in a normal response experiment
4. Multiple comparison approaches for normal response experiments
5. Problems involving a standard or control treatment in normal response experiments
6. Selection problems in two-factor normal response experiments
7. Selecting best treatments in single-factor Bernoulli response
8. Selection problems for categorical response experimentsReadership: Experimental scientists, engineers
From the large literature on ranking and selection problems, this book is focused on three types of procedures: selection procedure using the so-called indifference-zone approach, screening procedure and three types of multiple comparison procedures. Differently from the previous books in this field, this book is intended for the practitioners first stating clearly the goal of each procedure, then giving its sampling and terminal decision rules without getting into detailed mathematics. The tables are given for choosing sample size based on the probability of correct decision and the smallest difference worth detecting, and also the FORTRAN Programs when those tables are not available. Useful comments based on an extensive simulation are given for choosing one when several procedures are available for the same goal. Because of the chapter notes and bibliographies this book is also useful for statisticians for their further research.
Reviewer: Institute University of Tokyo Place Tokyo, Japan Name C. Hirotsu
Title MULTIVARIATE STATISTICAL ANALYSIS. Author N.C. Giri. Publisher New York: Dekker, 1996, pp. xii + 378, US$135.00. Contents:
1. Vector and matrix algebra
2. Groups and Jacobian of some transformations
3. Multivariate distributions and invariance
4. Properties of multivariate distributions
5. Estimators of parameters and their functions
6. Basic multivariate sampling distributions
7. Tests of hypotheses of mean vectors
8. Tests concerning covariance matrices and mean vectors
9. Discriminant analysis
10. Principal components
11. Canonical correlations
12. Factor analysisReadership: Graduate students in statistics, some graduate students in other disciplines
This is a book on classical multivariate statistics from the perspective of invariance to transformations. Emphasis is placed on tests and classical procedures. There is no coverage of (algorithm driven) techniques such as cluster analysis, ordination, multi-dimensional scaling, or optimal scaling methods. The limitations are illustrated by Chapter 9, on discriminant analysis, which begins with a discussion in terms of arbitrary distributions, but then focuses on methods based on normal distributions, though it does consider equal or unequal covariance matrices and more than two classes. The concluding paragraph of this chapter states 'the cases of non-normal and discrete distributions are equally important in practice' and then gives some references.
This is a formal, mathematical book, not an applied text, although there are some numerical examples. It would be suitable for students of mathematical statistics who want a grounding in a class of multivariate methods. For those for whom the mathematics is more of a means to an end, a book such as W.J. Krzanowski (1988), Principles of Multivariate Analysis: A User's Perspective, [Short Book reviews, Vol 8, p. 41] may be more helpful.
Reviewer: Institute The Open University Place Milton Keynes, U.K. Name D.J. Hand
Title STATISTICS AND ECONOMETRIC MODELS. Volume 1. General Concepts, Estimation, Production, and Algorithms. Volume 2. Testing, Confidence Regions, Model Selection, and Asymptotic T Author C. Gourieroux and A. Monfort. Translated by Quang Vuong. Cambridge Publisher University Press, 1995, pp. xvii + 504, pp. x + 526, ,50.00/US$69.95 Cloth; £17.95/ US$24.95 Paper, each volume. Contents:
Volume 1.
1. Models
2. Statistical problems and decision theory
3. Statistical information: Classical approach
4. Bayesian interpretations of sufficiency, ancillarity, and identification
5. Elements of estimation theory
6. Unbiased estimation
7. Maximum likelihood estimation
8. M-estimation
9. Method of moments and their generalizations
10. Estimation under equality constraints
11. Prediction
12. Bayesian estimation
13. Numerical procedures
Volume 2
14. Introduction to tests of hypotheses
15. Uniformly most powerful tests
16. Unbiased tests and invariant tests
17. Likelihood based tests
18. General asymptotic tests
19. Multiple tests
20. Set estimation and confidence regions
21. Inequality constraints: Estimation and testing
22. Non-nested models
23. Asymptotic efficiency
24. Asymptotic theory
Review of Linear Algebra and Matrix Calculus
Review of ProbabilityReadership: Theoretical statisticians, econometricians
These two important books, excellently translated from the French edition of 1989, provide a comprehensive account of the formal mathematical theory of statistics. A companion volume deals with the special problems of time series and dynamic models. Chapter 1 introduces principles of econometric model-ling. After that, although the brief illustrative examples are typically econometric, no special know-ledge of that subject is needed to read the book, which is thus accessible to a wide mathematical statistical audience. The mathematical level is careful with clear statement of regularity conditions and at the same time technical mathematical issues are not allowed to over-burden the discussion. The authors have an eclectic view of the subject. Although the book is primarily on the mathematical aspects of statistical theory, the occasional more verbal passages are strong.
In some ways the most interesting parts are on those issues which get more emphasis in the econometric literature than in general statistical writing and on issues to which the authors themselves have made important contributions. These include the generalized method of moments, the study of pseudo-maximum likelihood methods and non-nested hypotheses and the role of instrumental variables.
[Review of French edition Short Book Reviews, Vol. 9, p.44].
Reviewer: Institute Nuffield College Place Oxford, U.K. Name D.R. Cox
Title TIME SERIES MODELS. In Econometrics, Finance and Other Fields. Author D.R. Cox, D.V. Hinkley and O.E. Barndorff-Nielsen. (Eds.). Publisher London: Chapman and Hall, 1996, pp. xiv + 225, £30.00. Contents:
1. Statistical aspects of ARCH and stochastic volatility, by N.G. Shephard
2. Likelihood-based inference for co-integration of some non-stationary time series, by S. Johansen
3. Forecasting in macro-economics, by M.P. Clements and D.F. Hendry
4. Longitudinal panel data: An overview of current methodology, by N.M. Laird
5. Pricing by no arbitrage, by B.A. Jensen and J.A. NielsenReadership: Researchers
These are revised versions of the main papers from the second Séminaire Européen de Statistique on 'Likelihood, Time Series, with Econometrics and Other Applications', held at Nuffield College, Oxford, 1994.
The aim is to 'provide talented young researchers to get quickly to the forefront ... in areas of current major focus ... accordingly, the papers in this volume have a tutorial character'.
The applied examples add spice to these crisply written essays, distinguishing the volume from a set of subject surveys. Chapter 1 emphasizes univariate models, applies variants of ARCH and stochastics volatility (SV) models to financial data, and discusses the potential of SV and multivariate models in future research. Chapter 5, also about finance, differs from all other chapters by treating its topic without direct reference to data. It discusses discrete and continuous time complete market contingent claim models and the equivalence of the no arbitrage condition and the existence of an equivalent martingale measure for pricing assets.
Chapter 2 reviews the likelihood-based approach to testing and estimating co-integrated relationships in non-stationary time series. A purchasing power parity application illustrates the techniques. Chapter 3 catalogues various issues in forecasting multivariate time series, especially forecast accuracy, parameter consistency and intercept corrections. Chapter 4 contrasts two methods for estimating longitudinal panel data, generalized estimating equations and maximum likelihood. The relationship between child-hood obesity and coronary risk is estimated by each method.
Reviewer: Institute Queen's University Place Kingston, Canada Name A. Gregory, I.G. Morgan
Title BASIC PRINCIPLES OF STRUCTURAL EQUATION MODELLING: An Introduction to LISREL and EQS. Author R.O. Mueller. Publisher New York: Springer-Verlag, 1996, pp. xxviii + 229, US$239.95. Contents:
1. Linear regression and classical path analysis
2. Confirmatory factor analysis
3. General structural equation modelling
APPENDIX A: The SIMPLIS Command Language
APPENDIX B: Location, Dispersion and Association
APPENDIX C: Matrix Algebra
APPENDIX D: Descriptive Statistics for the SES Analysis
APPENDIX E: Descriptive Statistics for the HBI AnalysisReadership: Graduate students, applied researchers and teachers of Structural Equation Modelling
Structural Equation Modelling is widely used in the social sciences. This book serves as a useful introduction to the principles and techniques of Structural Equation Modelling and to commonly used software. It will be of most use to those who have some grounding in statistical methods but wish to explore further, either out of interest or to meet a pressing research need. The presentation takes the readers firmly by the hand and guides them through simple linear regression, via multiple regression to classical path analysis and on to confirmatory and exploratory factor analyses. The examples are based on a common set of data. At each step, the inputs and outputs of two common software packages, LISREL and EQS, are illustrated and interpreted. An Appendix shows the use of SIMPLIS (SIMPle LISrel). A most attractive feature is the reiteration of basic assumptions which underlie the use of the techniques and the emphasis on theoretical justification of the model. Interested readers will find a well-chosen collection of further reading lists.
Reviewer: Institute University of Bath Place Bath, U.K. Name B. Farbey
Title APPLIED STOCHASTIC PROCESSES. A BIOSTATISTICAL AND POPULATION ORIENTED APPROACH. Author S. Biswas. Publisher New Delhi, Wiley, 1995, pp. xiv + 427, £29.95. Contents:
1. Introduction to stochastic processes: Basic concept
2. Random walk and Markov processes
3. Non-Markov process and renewal theory
4. Martingales
5. Counter theory and age-replacement policy
6. Palm probability and its applications
7. Stochastic epidemic processes
8. Stochastic processes of clinical drug trials
9. Techniques of stochastic processes in mortality analysis - applications on life-table
10. Techniques of stochastic processes in fertility analysis
11. Techniques of stochastic processes for demographic analysis - population growth indices
12. Stochastic processes on survival and competing risk theory
13. Stochastic processes in geneticsReadership: Theoretical biostatisticians
This is a very methodological volume on the applications of stochastic processes to demographic processes (such as fertility and mortality) and to genetics.
The first six chapters define the fundamental principles of the theory of stochastic processes. The following chapters deal with specific applications and introduce the reader to a vast number of models, all presented in great detail and compared. The final chapter on stochastic processes in genetics is a particularly useful introduction to genetic epidemiology.
Reviewer: Institute London School of Hygiene and Tropical Medicine Place London, U.K. Name B.L. De Stavola
Title PATTERN RECOGNITION AND NEURAL NETWORKS. Author B.D. Ripley. Publisher Cambridge University Press, 1996, pp. xi + 403, £29.95/US$49.95. Contents:
1. Introduction and examples
2. Statistical decision theory
3. Linear discriminant analysis
4. Flexible discriminants
5. Feed-forward neural networks
6. Non-parametric methods
7. Tree-structured classifiers
8. Belief networks
9. Unsupervised methods
10. Finding good pattern featuresReadership: Statisticians, engineers, computer scientists, physicists
This book discusses several approaches to multivariate classification, starting with linear discriminant analysis and moving through to non-linear methods including neural networks. A particularly useful feature for the statistician is that many methods from computer science are characterized in statistical terminology. The book is basically theoretical: the derivations and proofs are presented from first principles and are statistically interesting and rigorous without being pedantic. At the same time, several data-based examples are used throughout, illustrated with computer plots. The combination of theory and examples makes this a unique and interesting book.
Reviewer: Institute University of California Place Berkeley, U.S.A. Name A. Gelman
Title INTRODUCTORY STATISTICS: A MODELLING APPROACH. Author J.K. Lindsey. Publisher Oxford: Clarendon, 1995, pp. xi + 214, £19.50. Contents:
1. Basic concepts
2. Categorical data
3. Inference
4. Probability distributions
5. Normal regression and ANOVA
6. Dependent responses
7. Where to now?Readership: Students of medicine, biology, or social science who need to use statistics to design surveys or experiments and analyze the resulting data
The book is based on a course the author has presented to social science students for almost twenty years and can be covered in about sixty hours of lectures plus practical work. The material can be taught with a computer or with a hand calculator; Lindsey argues that it is essential that the beginning student sees exactly how the basic results are obtained. The author believes that a 'feel for the aims of statistics should be clearly communicated before elaborate mathematical justifications are presented', whether the students are studying statistics as their main subject or as a subsidiary subject. I agree with this view. If it were generally adopted it might put the subject of statistics in its rightful place as the most fundamental tool for scientific investigation, instead of being regarded, as it all too often is, as merely a second class kind of mathematics.
The basic philosophy of the book is that of the construction of models to describe the structure of data, with the probability distribution being the fundamental building block, and that a model describes how the form of such a distribution differs in different subpopulations. Inference from the sample to the population plays a secondary role. The central role played by probability distributions is illustrated by the fact that Chapter 4 covers sixteen distributions. The examples use real sets of data although the author does recommend that these are replaced by examples from other courses which the student is taking concurrently. Each chapter is concluded with a set of exercises matching the text of the book, data analytic rather than mathematical.
The book is concise enough to appeal to students for whom statistics is a subsidiary subject, but in my experience many such students, for example psychologists, would find some of the mathematical expressions hard going. For the more mathematically literate student, however, I would recommend this as
an introduction to the subject.
Reviewer: Institute The Open University Place Milton Keynes, U.K. Name D.J. Hand
Title MODELLING FREQUENCY AND COUNT DATA. Author J.K. Lindsey. Publisher Oxford: Clarendon, 1995, pp. ix + 291, ,30.00. Contents:
PART I : Frequency Data
1. One-way frequency tables
2. Larger tables
3. Regression models
4. Ordinal variables
5. Zero frequencies
6. Fitting distributions
PART II : Count Data
7. Counting processes
8. Markov chains
9. Structured transition matrices
10. Overdispersion and cluster modelsReadership: Graduates taking courses in statistics and applied statistics, senior undergraduates studying these disciplines
Lindsey distinguishes between frequencies of events, the number of times the events occur to independent individuals, and counts, the number of times the events occur to the same individual. This distinct-ion, the use of models to find structure in data, and the fact that real data is discrete and never continuous, form the philosophical basis of this book. It is best described as a modern applied statistics book, not shying away from the mathematics where it is necessary, but presenting its discussion via statistical models described using the Wilkinson and Rogers notation and fitted using a common software package. The examples in the book were analyzed using GLIM4, supplemented by GLIM macros, included in the appendix, for those cases which could not be fitted as standard generalized linear models. This will provide a good book on which to base a course, though it will be well to supplement it by lectures or other tutor contact to explain the odd throwaway line such as (p.74) 'the absolute deviance for a binary data problem has no interpretation for goodness-of-fit, because it depends only on the fitted values' which in my experience students find puzzling at first. Many sets of data given in the exercises conclude each chapter.
Reviewer: Institute The Open University Place Milton Keynes, U.K. Name D.J. Hand
Title SURVIVAL ANALYSIS. A Practical Approach. Author M.K.B. Parmar and D. Machin. Publisher Chichester, U.K.: Wiley, 1995, pp. xi + 255, £29.95. Contents:
1. Introduction and review of statistical concepts
2. Survival curves
3. The exponential and Weibull distributions
4. Comparison of two survival curves
5. More than two groups
6. Cox's proportional hazards models
7. Selecting variables within a Cox model
8. Time-dependent variables
9. Prognostic indices
10. Sample sizes for survival studies
11. Miscellaneous topicsReadership: Biostatisticians, medical researchers
The unique feature of this book is the extremely detailed exposition of the calculations involved in survival analysis data. The arithmetic of methods such as the Kaplan-Meier estimate of the survival curve and log rank test are displayed in full using data drawn from recent medical literature. For more advanced methods, such as fitting a proportional hazards model, the authors show as far as possible how parts of the output of a computer package are calculated. From this point of view the text would be useful to a non-statistician who would like to mimic the calculations on their own data or who wants to understand how the numbers produced from a package are arrived at.
The coverage of the subject is wide, as the table of contents shows, and the material is presented with strong emphasis on showing how methods are implemented. However, one would not gain an understanding of the concepts of survival analysis from this book nor does one find a discussion of the many issues that arise in the application of these methods. For this, one would need to consult texts such as those of D. Collet, Modelling Survival Data in Medical Research [Short Book Reviews, Vol. 14, p.25] or E. Marubini and M.G. Valsecchi, Analysing Survival Data From Clinical Trials and Observational Studies. [Short Book Reviews, Vol. 15, p.23].
There is a particularly unfortunate and surely unintended verbal definition of the survival function at time t as the proportion of the total area beneath the death density to the left of t. This slip is com-pounded by the labelling of the diagram. The mathematical definition is given correctly.
Reviewer: Institute University of Cape Town Place Rondebosch, South Africa Name J.M. Juritz
Title ASYMPTOTIC EFFICIENCY OF NONPARAMETRIC TESTS. Author Y. Nikitin. Publisher Cambridge University Press, 1995, pp. xvi + 274, ,32.50/US$49.95 Contents:
Introduction
1. Asymptotic efficiency of statistical tests and mathematical means for its computation
2. Asymptotic efficiency of non-parametric goodness-of-fit tests
3. Asymptotic efficiency of non-parametric homogeneity tests
4. Asymptotic efficiency of non-parametric symmetry tests
5. Asymptotic efficiency of non-parametric independence tests
6. Local asymptotic optimality of non-parametric tests and the characterization of distributionsReadership: Mathematical statisticians
The concept of efficiency is very important in comparing tests, say for some null hypothesis H:0=00. The relative efficiency of some test with respect to a competing one is given by the ratio of the sample sizes needed to obtain power â under level á at the alternative value 0. Since exact computation of such a quantity is complicated, various concepts of asymptotic relative efficiency (ARE) have been introduced by keeping some of the parameters fixed and let-ting the others tend to a limit. For example: Pitman ARE (0 ? 00), Hodges-Lehmann ARE (â ? 1), Bahadur ARE (á ? 0), etc. The author gives a unifying treatment of various ARE's for Kolomogorov-Smirnov and Cramér-von Mises non-parametric tests and their variants as well as linear rank tests. These calculations require various mathematical techniques and of course large deviation theorems of different types. The author has been very active in this area for at least twenty years and has successfully brought together a large number of papers including many references from the Russian literature.
Reviewer: Institute Limburgs Universitair Centrum Place Diepenbeek, Belgium Name N. Veraverbeke
Title EFFICIENT AND INEFFICIENT ESTIMATION IN SEMIPARAMETRIC MODELS. Author M.J. van der Laan. Publisher Amsterdam: Stichting Mathematisch Centrum, 1995, pp. vi + 219, DFL.50.00. Contents:
Introduction
1. Basic theory
PART I : Efficiency Theory and Applications for (Non parametric) Maximum Likelihood Estimators
2. Efficiency theory for the (NP)MLE and an identity for linear parameters in convex models
3. Efficiency of the sieved-NPMLE for a class of missing data models with applications
4. Efficient estimation in the bivariate censoring model and repairing NPMLE
5. Efficiency of the NPMLE in the line-segment problem
PART II: Inefficient Estimation in Semiparametric Models
6. Inefficient estimators of the bivariate survival function in the bivariate censoring model
7. Modified EM-Estimator of the bivariate survival functionReadership: Mathematical statisticians, graduate students in mathematical statistics
This tract is, essentially, a self-contained research monograph on the theory of estimation in semi-parametric models. Chapter 1 covers the relevant theories of weak convergence, empirical processes, efficiency and the so-called functional delta-method that form a basis for this two-part exposition. The first part covers general efficiency theory for MLE and ap-plies this theory to a general class of missing data models. The second part studies the construction of inefficient estimators in the bivariate censoring model. These estimators are of interest because they are easy to compute, have a good practical performance, and are robust to changes in the underlying distribution of the samples.
Reviewer: Institute Carleton University Place Ottawa, Canada Name M. Csörgö
Title NON-REGULAR STATISTICAL ESTIMATION. Author M. Akahira and K. Takeuchi. Publisher New York: Springer-Verlag, 1995, pp. viii + 184. Contents:
1. General discussion on unbiased estimation
2. Lower bound for the variance of unbiased estimators
3. Amounts of information and the minimum variance unbiased estimation
4. Loss of information associated with the order statistics and related estimators in the case of double exponential distributions
5. Estimation of a common parameter for pooled samples from the uniform distributions and the double exponential distributions
6. Higher order asymptotics in estimation for two- sided Weibull type distributions
7. "3/2-th" and second order asymptotics of the generalized Bayesian estimators for a family of truncated distributions
Supplement: The bound for the asymptotic distribution of estimators when the maximum order of consistency depends on a parameterReadership: Mathematical statisticians
Anyone teaching a course in statistical inference knows about the many regularity conditions that are involved in for instance the asymptotic theory of maximum-likelihood estimation. Elementary courses usually assume "sufficient regularity" while most mathematically oriented courses formulate these regularity conditions in a rigorous way. This monograph deals with the statistical estimation theory in the so-called "non-regular" cases, i.e. cases where some of the traditional restricting regularity conditions fail. Both authors have written an impressive number of papers in this area, and now come up with a systematic presentation of their results. They give extensive discussions on a number of important topics for which I can refer to the table of contents since they are sufficiently well formulated there. The book is written with care and there are many examples that are "non-regular", but far from "pathological". The book is one of the very few ones dealing with these topics, both in the finite and in the infinite sample situation.
Reviewer: Institute Limburgs Universitair Centrum Place Diepenbeek, Belgium Name N. Veraverbeke
Title GREEN, BROWN, AND PROBABILITY. Author K.L. Chung. Publisher Singapore: World Scientific, 1995, pp. xii + 106. Contents:
1. Green's ideas
2. Probability and potential
3. Process
4. Random time
5. Markov property
6. Brownian construct
7. The trouble with boundary
8. Return to Green
9. Strong Markov property
10. Transience
11. Last but not least
12. Least energyReadership: Graduates in probability theory
This is the story of the birth of Brownian motion told by one of the masters in the field. The physics underlying the original construction (Einstein) is never far away. At the same time, the author moves quickly into some of the more advanced properties al-ways pointing the reader to unexpected results and potential caveats. George Green's work on the equilibrium of electric and magnetic fields is a recurring theme in many disguises. The (graduate) student will like the historical perspective together with the more physical background. Various rather personal comments by the author add more than just a pinch of salt. This book is to be recommended to all interested in Brownian motion and potential theory.
Reviewer: Institute ETH-Zürich Place Zürich, Switzerland Name P.A.L. Embrechts
Title STOCHASTIC GEOMETRY AND ITS APPLICATIONS, 2nd edition. Author D. Stoyan, W.S. Kendall and J. Mecke. Publisher Chichester, U.K.: Wiley, 1995, pp. xix + 436, £50.00. Contents:
1. Mathematical foundations
2. Point processes I - The Poisson point process
3. Random closed sets I - The Boolean model
4. Point processes II - General theory
5. Point processes III - Construction of models
6. Random closed sets II - The general case
7. Random measures
8. Random processes of geometrical objects
9. Fibre and surface processes
10. Random tessellations
11. StereologyReadership: Probabilists, geometers, stereologists, scientists using quantitative methods in geology, biology, microscopy and materials science
The first edition, 1987, firmly established stochastic geometry as the mathematics for describing, characterising and investigating the random spatial process and patterns such as arise in geology, biology, microscopy and materials science. Although the statistical requirements are addressed by descriptions of estimators, tests and simulations, the emphasis is on the probability modelling. A justification that could have been offered is that the statistical theory is not yet sufficiently developed to allow for definitive rules and recommendations. Fractals, random shapes and integral geometry are given only a brief coverage.
This new edition incorporates new work, though this seems in the main to be further references added to the text. The reviewer of the first edition [Short Book Reviews, Vol. 7, pp. 42] referred to the austere style. While many minor changes have been made ("ovoids" are now "convex bodies", for example), what is most immediately noticeable is that the book has been given a facelift. The type has been completely reset, the book is printed on better paper, and many of the figures have been redrawn.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name R. Coleman
Title DISCRETE-TIME MARKOV CONTROL PROCESSES. Basic Optimality Criterion. Author O. Hernández-Lerma and J.B. Lasserre. Publisher New York: Springer-Verlag, New York, 1996, pp. xiv + 216, US$54.95. Contents:
1. Introduction and summary
2. Markov control processes
3. Finite horizon problems
4. Infinite-horizon discounted-cost problems
5. Long-run average-cost problems
6. Linear programming formulation
APPENDIX A: Miscellaneous Results
APPENDIX B: Conditional Expectation
APPENDIX C: Stochastic Kernels
APPENDIX D: Multi-Functions and Selectors
APPENDIX E: Convergence of Probability MeasuresReadership: Researchers or advanced graduate students in stochastic control theory or applied probability
This book is Part 1 of a planned two-volume series dealing with the theory of discrete-time Markov control processes. A good background in real analysis and measure theoretic probability is required to read this book. The main motivation for the book is to treat rather general controlled Markov processes which may have uncountable state space, unbounded costs-per-stage and/or non-contact control restraints. The book is re-commended to anyone wishing to catch up with recent theoretical developments in the area of controlled Markov processes. Although not explicitly treated in the book, the application areas are extensive and include manufacturing economics, and environmental problems.
Reviewer: Institute University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONAL SPACE. Author G. Kallianpur and J. Xiong. Publisher Hayward, California: Institute of Mathematical Statistics, 1995, pp. vi + 342. Contents:
1. Topological vector spaces
2. Probability measures
3. Stochastic integrals
4. SPDE
5. SDE in Hilbert space
6. Stochastic differential equations
7. Environmental pollution
8. Diffusion processes
9. Interacting systems
10. Large deviationsReadership: Researchers and advanced students in probability
This substantial volume provides a coherent and reasonably self-contained treatment of the theory of probability models based on systems of stochastic ordinary or partial differential equations in infinite-
dimensional spaces. It is an amplification of a special series of lectures given by the first author. The topic is one of significant and growing interest within probability, due in great part to the increasing number of complex phenomena whose stochastic modelling is amenable to these methods. In this book, the wide applicability is illustrated through models of environ-mental pollution and infinite particle systems. Of particular interest in this presentation is the parallel emphasis given to differential equations driven by
Poisson-like atomic measures in addition to that given to those driven by the more common white noise random measures. The book has been carefully prepared and represents a scholarly and inexpensive addition to the advanced monographs available on stochastic differential equations.
Reviewer: Institute University of Washington Place Seattle, U.S.A. Name R. Pyke
Title SEQUENTIAL STOCHASTIC OPTIMIZATION. Author R. Cairoli and R.C. Dalang. Publisher New York: Wiley, 1996, pp. xi + 327, £45.00. Contents:
1. Preliminaries
2. Sums of independent random variables
3. Optimal stopping
4. Reduction to a single dimension
5. Accessibility and filtration structure
6. Sequential sampling
7. Optimal sequential control
8. Multi-armed bandits
9. The Markovian case
10. Optimal switching between two random walksReadership: Graduate students and mathematicians working in probability theory
Sequential stochastic optimization is the study of random sequential processes which are affected by the choices of a controller. At each stage, the controller chooses from a finite set of alternatives based upon the observation of the process to date. The choices in turn affect the probability distributions from which later events in the sequence are chosen. There are costs (or rewards) associated with each action and the objective is to minimize costs, i.e. maximize rewards. The book begins with a study of optimal stopping points, including many new and recent results in this area. These results are presented in a very general framework. This treatment will be most appreciated by researchers with a solid background in measure theory and probability. The authors then pre-sent applications of this theory to classical stochastic optimization problems in sequential sampling and Markov processes as well as to multi-armed bandits and processes switching between two random walks.
Reviewer: Institute University of Paris 6 Place Paris, France Name B. Reed
Title XploRe: AN INTERACTIVE STATISTICAL COMPUTING ENVIRONMENT. Author W. Härdle, S. Klinke and B.A. Turlach (Eds.). Publisher New York: Springer-Verlag, pp. xvi + 387, DM.74.00/ÖS.577.20/Sw.fr.71.50. Contents:
PART I : A Beginner's Course
1. Un amuse-gueule by W. Härdle
2. An XploRe tutorial by W. Härdle
3. The integrated working environment by C. Gajewski
PART II : XploRe in Use
4. Graphical aids for statistical data analysis by S. Klinke and C. Ritter
5. Density and regression smoothing by J. Fan and M. Müller
6. Bandwidth selection in density estimation by M. Bianchi
7. Interactive graphics for teaching simple statistics by I. Proença
8. XClust: Clustering in an interactive way by H.-J. Mucha
9. Exploratory projection pursuit by S. Klinke and J. Polzehl
10. Generalized linear models by J. Hilbe and B.H. Turlach
11. Additive modeling by T. Kötter and B.H. Turlach
12. Comparing parametric and semiparametric binary response models by I. Proença and K. Werwatz
13. Approximate methods for regression models with errors in covariates by R.J. Carroll and H. Küchenoff
14. Nonlinear time series analysis by R. Chen and C. Hafner
15. Un Digestif by W. Härdle and S. KlinkeReadership: Users of XploRe
XploRe is a computer package for doing statistical computations and graphics. The first three chapters of this book give a short introduction to using it, and the following twelve illustrate implementation of a reasonably wide variety of techniques.
I am not an XploRe user, and I was hoping to find in this book a reason why I should become one. I was disappointed, however, in that there is no overview or statement of purpose for XploRe. What were the authors trying to achieve with it? What is it especially good at? I had to guess: as a computing environ-ment, XploRe appears to be most closely a competitor of S (R.A. Becker, J.M. Chambers and A.R. Wilks, 1988 [Short Book Reviews, Vol. 9, p.2]) and Lisp-Stat, (L. Tierney, 1989 [Short Book Reviews, Vol. 11, p.46.)]: it is programmable and extendable, and is aimed at developers of new techniques. Unlike S, it does not attempt to produce publication quality graphics. Like Lisp-Stat, it is possible to program it to give moving pictures. Like both, it is not designed for routine use of standard techniques: data handling appears to be far more limited than in a package like SAS. I could not tell from this book whether there was any area in which XploRe excels.
For someone who already uses XploRe, I think this book would be more useful. The twelve chapters of examples introduce and show implementations of a variety of techniques. It could be an easier read, though: in many places the English is awkward, and the use of colour plates for some figures makes no sense. In one example (Fig 4.6) the caption indicates colour where there is none, and in several cases, for example, Figures 5.1 and 5.4, colour is used for no apparent reason.
Reviewer: Institute Queen's University Place Kingston, Canada Name D.J. Murdoch
Title THE NATURE OF STATISTICAL LEARNING THEORY. Author V.N. Vapnik. Publisher New York: Springer-Verlag, 1995, pp. xv + 188, US$39.95. Contents:
Introduction: Four periods in the research of the learning problem
1. Setting of the learning problem
2. Consistency of learning process
3. Bounds on the rate of convergence of learning process
4. Controlling the generalization ability of learning process
5. Constructing learning algorithms
Conclusions: What is important in learning theoryReadership: General readers with good statistical background
The book is clearly written and can be considered as a very reasonable compromise between simplicity and mathematical accuracy. With some constructive scepticism, the author considers a few hot topics such as "Artificial Intelligence" and "Neural Networks". Obviously he gravitates to the idea that most of the corresponding findings are a "reopening" of some well-established results from mathematical statistics and probability theory. The phrase in the Introduction "First the hardliners changed the terminology" is a very accurate reflection of the author's view of the above-mentioned areas. This interesting book helps a reader to understand the interconnections between various streams in the empirical modeling realm and may be recommended to any reader who feels lost in modern terminology.
Reviewer: Institute Oak Ridge National Laboratory Place Oak Ridge, U.S.A. Name V.V. Fedorov
Title STATISTICAL DISCLOSURE CONTROL IN PRACTICE. Author L. Willenberg and T. de Waal. Publisher New York: Springer-Verlag, 1996, pp. xiii + 152, US$34.95. Contents:
1. Introduction to statistical disclosure control
2. Principles
3. Policies and case studies
4. Microdata
5. Microdata: Backgrounds
6. Tabular data
7. Tabular data: Backgrounds
8. Loose endsReadership: Official statisticians, others who disseminate statistical information
The authors main aim is to discuss various aspects associated with disseminating personal or business data. The data may be in the form of individual data, microdata, or in aggregate form, tabular data.
For both microdata and tabular data the authors identify two problems: (i) how to properly assess the disclosure risk and (ii) how to efficiently produce safe micro and tabular data. The important point in disseminating data is to ensure that individuals and other entities cannot be recognized.
In the eight chapters of the book the authors successfully bring together practical methods of solving these two problems and hence make a significant contribution to the literature on statistical dis-closure control.
Reviewer: Institute United Nations Place New York, U.S.A. Name O.A.Y. Jackson
Title ASSESSMENT: PROBLEMS, DEVELOPMENTS AND STATISTICAL ISSUES. Author H. Goldstein and T. Lewis (Eds.). Publisher Chichester, U.K.: 1996, pp. xvi + 269, £45.00. Contents:
1. The scope of assessment, by H. Goldstein and T. Lewis
2. Assessment: Some historical perspectives, by G. Sutherland
3. Assessment and learning: Power or partnership? by P. Broadfoot
4. Statistical and psychometric models for assessment, by H. Goldstein
5. Defining, setting and maintaining standards in curriculum-embedded examinations: Judgemental and statistical approaches, by M.J. Cresswell
6. Group differences and bias in assessment, by H. Goldstein
7. Moderation procedures and the maintenance of assessment standards, by T. Lewis
8. Errors in grading and forensic issues in higher education, by D.B. McLay
9. The use of assessment to compare institutions, by J. Gray
10. The statistical analysis of institution-based data, by G. Woodhouse and H. Goldstein
11. The extent and growth of educational testing in the United States: 1956-1994, by G.F. Madaus and A.E. Raczek
12. The integrity of public examinations in developing countries, by V. Greaney and T. Kellaghan
13. Large-scale assessment programmes in different countries and international comparisons, by L.D. McLean
14. Vocational assessment, by A. Wolf
15. Assessment in the workplace, by R. VincentReadership: Teachers, educationists, policy-makers, personnel managers, general readers
Assessment plays a role of ever-increasing importance in society, especially now it has become so involved in issues of public accountability. This read-able book is essentially a collection of informative but relatively non-technical essays covering a wide range of topics. Many issues receive a good airing. Two areas of major concern which are very thoroughly discussed are hidden assumptions which underlie so many assessment procedures and the increasing and dangerous tendency to use assessments designed and carried out for one purpose to achieve a different one, for ex-ample, use of the results of assessments of individuals to rank institutions. Statistical issues are presented in a descriptive and largely non-specialist way with very little use of mathematical symbols and terminology. The book deserves a wide readership, particularly including those who confidently base political and social judgements on assessment results.
Reviewer: Institute University of St. Andrews Place St. Andrews, U.K. Name C.D. Kemp
Title LIFETIME DATA: MODELS IN RELIABILITY AND SURVIVAL ANALYSIS. Author N.P. Jewell, A.C. Kimber, M.-L. T. Lee and G.A. Whitmore (Ed.). Publisher Dordrecht, The Netherlands: Kluwer, 1996, pp. xi + 409, Dfl.290.00/US$159.00/,104.00. Sample of Contents:
Initial conditions problem in event history analysis: An indirect inference procedure, by M.Y. An Analysis of survival data under competing risks with missing cause of death information: Application and implications for study design, by J.W. Andersen, E.J. Goetghebeur and L. Ryan
Models for degradation processes and event times based on Gaussian processes, by K. Doksum and S.L.T. Normand
Cure mixture models in breast cancer survival studies, by N.H. Gordon
A general approach to derive chi-square type of goodness-of-fit tests for lifetime data, by S. Hawala and J.L. Wang
Dynamic reliability models, by M. Hollander and E.A. Peña
Generalizations of current status data with applications, by N.P. Jewell and M. van der Laan
Historical controls and model survival analysis, by N. Keiding
A random effects model for multivariate life data, by A.C. Kimber
Intermediate clinical events, surrogate markers and survival, by M. Lefkopoulou and M. Zelen
Statistical methods for dependent competing risks, by M.L. Moeschberger and J.P. Klein
Statistical models for quality of life measures, by Y. Palesch and A.J. Gross
Efficiently weighted estimating equations with application to proportional excess hazards, by P. Sasieni
Assessing Gamma frailty models for clustered failure time data, by J.H. Shih and T.A. Louis
Dependent competing risks with time-dependent covariates, by E.V. Slud and L. Kopylev
Modeling frailty in manufacturing processes, by J.T. Wassell, G.W. Kulczycki and E.S. MoyerReadership: Those working on the development or application of statistical methods for lifetime data
This book contains a selection of fifty-three papers based on presentations given at the "1994 Inter-national Research Conference on Lifetime Data Models in Reliability and Survival Analysis", held at Harvard University. A sample of sixteen papers are listed. Many areas of current interest in lifetime data analysis are examined in this book, for example, frailty models, multivariate failure time data, multi-state models, censored data. Advances motivated by biomedical, industrial and other areas are well represented. Several papers conclude with remarks on open questions making this book valuable both as a reference text and as a stimulus for future research. This book will make a worthwhile addition to the shelf of any statistician with an interest in lifetime data.
Reviewer: Institute University of Waterloo Place Waterloo, Canada Name R.J. Cook
Title MODELS FOR INFECTIOUS HUMAN DISEASES: THEIR STRUCTURE AND RELATION TO DATA. Author V. Isham and G. Medley (Eds.). Publisher Cambridge University Press, 1996, pp. xxiii + 490, £45.00/US$59.95. Contents:
PART 1: Transmissible Diseases with Long Development Times and Vaccination Strategies
PART 2: Dynamics of Immunity (The Development of Disease Within Individuals)
PART 3: Population Heterogeneity (Mixing)
PART 4: Consequences of Treatment Interventions.
PART 5: PredictionReadership: Statisticians, epidemiologists, mathematical modellers
The University of Cambridge Isaac Newton Institute sponsored a research programme on Epidemic Models: Their Structure and Relation to Data, from January to June 1993. This volume consists of papers presented at an international workshop on human diseases, as part of the research programme. There were about one hundred and fifty participants at the work-shop. The aims of the editors include encouraging a variety of interactions, as between AIDS research and other epidemiology, between transmissible and non-transmissible diseases, and between practical and theoretical studies. The volume contains invited and contributed papers, together with written versions of discussion, grouped under the five themes. Typically, contributed papers are only two to three pages long.
In 1996, a World Health Organization report estimated that seventeen million deaths a year are due to infectious diseases, of which at least thirty have risen during the last twenty years. This clearly demonstrates the importance of the work described in this edition, and the need, emphasised by the editors, for sound methods of prediction.
Reviewer: Institute University of Kent Place Canterbury, U.K. Name B.J.T. Morgan
Title BAYESIAN BIOSTATISTICS. Author D.A. Berry and D.K. Stangl (Eds.). Publisher New York: Dekker, 1996, pp. xii + 675, US$165.00. Contents:
PART I : General Overview
1. Bayesian methods in health-related research, by D.A. Berry and D.K. Stangl
2. Bayesian approaches to randomized trials, by D.J. Spiegelhalter, L.S. Freedman and M.K.B. Parmar
3. Bayesian epidemiology, by D. Ashby and J.L. Hutton
PART II : Assessing Probabilities
4. Elicitation of prior distributions, by K. Chaloner
5. Priors for the design and analysis of clinical trials, by J.B. Kadane and L.J. Wolfson
PART III: Decision Problems
6. A Weibull model for survival data: Using prediction to decide when to stop a clinical trial, by J. Qian, D.K. Stangl and S.George
7. Decision models in clinical recommendations development: The stroke prevention policy model, by G. Parmigiani, M. Ancukiewicz and D. Matchar
8. Dose-response analysis of toxic chemicals, by V. Hasselblad and A.M. Jarabek
9. Expected utility as a policy-making tool: An environmental health example, by L.J. Wolfson, J.B. Kadane and M.J. Small
PART IV : Design
10. Bayesian hypothesis testing: Interim analysis of clinical trial evaluating phenyton for prophylaxis of early post-traumatic seizures in children, by R.J. Lewis
11. Inference and design strategies for a hierarchical logistic regression model, by M. Clyde, P. Müller and G. Parmigiani
PART V : Model Selection
12. Model selection for generalized linear models via GLIB: Application to nutrition and breast cancer, by A.E. Raftery and S. Richardson
PART VI : Hierarchical Models
13. Bayesian analysis of population pharmacokinetic and instantaneous pharmacodynamic relationships, by A. Racine-Poon and J. Wakefield
14. Bayesian and frequentist analyses of an in vivo experiment in tumor hemodynamics, by R. D. Wolfinger and G.L. Rosner
15. Bayesian meta-analysis of randomized trials using graphical models and BUGS, by T.C. Smith, D.J. Spiegelhalter and M.K.B. Parmar
16. Hierarchical analysis of continuous-time survival models, by D.K. Stangl
17. Hierarchical Bayesian linear models for assessing the effect of extreme cold weather on schizophrenic births, by W. DuMouchel, C. Waternaux and D. Kinney
18. Fitting and checking a two-level Poisson model: Modeling patient mortality rates in heart transplant patients, by C.L. Christiansen and C.N. Morris
PART VII: Other Topics
19. Analyzing rodent tumorigenicity experiments using expert knowledge, by J.C. Lindsey and L.M. Ryan
20. Assessing drug interactions: Tamoxifen and Cyclophosphamide, by K. Abrams, D. Ashby, J. Houghton and D. Riley
21. Bayesian subset analysis of a clinical trial for the treatment of HIV infections, by R. Simon, D.O. Dixon, and B. Freidlin
22. Bayesian modeling of binary repeated measures data with application to crossover trials, by J. Albert and S. Chib
23. A comparative study of perinatal mortality using a two-component mixture model, by P. Dellaportas, D.A. Stephens, A.F.M. Smith, and I. Guttman
24. Change-point analysis of a randomized trial on the effects of calcium supplementation on blood pressure, by L. Joseph, D.B. Wolfson, R. du Berger and R.M. Lyle
25. Bayesian predictive inference for a binary random variable: Survey estimation of the quality of care that radiation therapy patients receive, by M. Racz and J. SedranskReadership: Applied statisticians, biostatisticians, students
This excellent if pricy compilation consists of twenty-five chapters written by an impressive array of authors. The main focus of each chapter is a substantive medical question. The three chapters comprising the General Overview are broad and form a good backdrop to more advanced topics. They are: Bayesian methods in health-related research, Bayesian approaches to randomized trials and Bayesian epidemiology. The other chapters are often more specialized but cover a very wide range of topics of current interest.
Reviewer: Institute University of Kent Place Canterbury, UK Name P.J. Brown
Title MULTIVARIATE GEOSTATISTICS. AN INTRODUCTION WITH APPLICATIONS. Author H. Wackernagel. Publisher Berlin: Springer Verlag, 1995, pp. xiv + 256, US$59.00. Contents:
Introduction
1. Preliminaries
2. Geostatistics
3. Multivariate analysis
4. Multivariate geostatistics
5. Non-stationary geostatisticsReadership: Researchers, lecturers and students, statisticians
While it is never stated explicitly, the author has a tendency to consider "geostatistics'" and "kriging" as synonyms. I think that "Multivariate Kriging" would be a better title, which more accurately reflects the content. Through the entire book, the author has tried very hard to make the reader's intui-tion work and mostly he perfectly succeeds in this mission. For readers, even with a relatively modest statistical background, the direct comparison of the kriging approach with the classical results of linear estimation and prediction theory would help enormously in the deeper understanding of the discussed results. A few appendices make the book more self-consistent. Only one of them, in which covariance and variagram models are considered, differs from the standard collection of appendices attached to almost any book in applied statistics. Without any doubt the book will find an extensive readership including serious practitioners. I will keep it as a rather comprehensive and well-written text on kriging.
Reviewer: Institute Oak Ridge National Laboratory Place Oak Ridge, U.S.A. Name V.V. Fedorov
Title VARIOWIN. Software for Spatial Data Analysis in 2D. Author Y. Pannatier. Publisher New York: Springer-Verlag, 1996, pp. ix + 91 + disk, US$49.95. Contents:
1. Introduction
2. Quick start
3. Construction of a pair comparison file (PCF) with Prevar 2D
4. Vario2D with PCF - A program for interactive exploratory variography
5. Model - Interactive variogram modeling
6. Files used within VARIOWN 2.2
APPENDIX A: Geostatistical ConceptsReadership: Researchers, statisticians and students with special interest in spatial analysis
This book is the instruction manual for a package for analyzing spatial data. The package, VARIOWN, enables one to model the spatial continuity of one variable or the joined spatial continuity of two variables. The variogram, the standardized variogram, the covariance, the correlogram and the madogram are used to measure spatial continuity. The main advantage of this package is the possibility to produce a two-dimensional nested model of spatial continuity in an interactive way. The nugget effect model, that used to model a discontinuity at the origin, the spherical model, the exponential model, the Gaussian model and the power model are used to form the two-dimensional nested model of spatial continuity.
The package consists of four separate components. The first program builds a pair comparison file, the second program is used for spatial data analysis, the third program is used for producing a pixel map. The graphical features of the package, including variogram surfaces, variogram clouds, sample maps, are good. There is no special editor for the raw data, which is not very convenient for the user, and the help-system could be improved.
The sequence of the material in the book is not good. The first chapter should have been a description of the possible measures of spatial continuity, which is now in Chapter 4 and in the Appendix. The second chapter should have been a description of the nested models of the spatial continuity (Chapter 5) and the geostatistical example (Appendix), and only after that the package should have been described.
For those who have other books on two-dimensional spatial analysis this book and package will be useful.
Reviewer: Institute Sevastopol State Technical University Place Sevastopol, Ukraine Name A.V. Tsukanov
Title A PROBABILISTIC THEORY OF PATTERN RECOGNITION. Author L. Devroye, L. Györfi and G. Lugosi. Publisher New York: Springer-Verlag, 1996, pp. xv + 636, ,46.00/US$69.00 Contents:
1. Introduction
2. The Bayes error
3. Inequalities and alternate distance measures
4. Linear discrimination
5. Nearest neighbor rules
6. Consistency
7. Slow rates of convergence
8. Error estimation
9. The regular histogram rule
10. Kernel rules
11. Consistency of the k-nearest neighbor rule
12. Vapnik-Chervonenkis theory
13. Combinatorial aspects of Vapnik-Chervonenkis theory
14. Lower bounds for empirical classifier selection
15. The maximum likelihood principle
16. Parametric classification
17. Generalized linear discrimination
18. Complexity regularization
19. Condensed and edited nearest neighbor rules
20. Tree classifiers
21. Data-dependent partitioning
22. Splitting the data
23. The resubstitution estimate
24. Deleted estimates of the error probability
25. Automatic kernel rules
26. Automatic nearest neighbor rules
27. Hypercubes and discrete spaces
28. Epsilon entropy and totally bounded sets
29. Uniform laws of large numbers
30. Neural networks
31. Other error estimates
32. Feature extractionReadership: Specialists in nonparametric statistics. Students of computational learning theory and Vapnik's statistical theory of learning
From the introduction: `This book is only a start. Use it as a toy C read some proofs, enjoy some inequalities, learn new tricks, and study the art of camouflaging one problem to look like another. Learn for the sake of learning. ... The methods gleaned from this text must be supplemented with a healthy dose of engineering savvy.' In that spirit, I enjoyed reading this book. It is easy to misunderstand the title C the book presents a collection of techniques for problems of what is sometimes called learnability. The emphasis is on distribution-free large-sample consistency re-sults for a binary classification problem, often for rules whose computational complexity appears prohibi-tive. Many of the most technical details are left to exercises (without hints), yet the results presented are often not the best known, the authors seeming more interested in the techniques. In more than one sense, this book demonstrates that learning can be hard.
Reviewer: Institute University of Oxford Place Oxford, U.K. Name B.D. Ripley
Title NEURAL NETWORKS AND QUALITATIVE PHYSICS. A VIABILITY APPROACH. Author J.-P. Aubin. Publisher Cambridge University Press, 1996, pp. xvii + 283, £29.95/US$ 49.95. Contents:
1. Neural networks: A control approach
2. Pseudoinverses and tensor products
3. Associative memories
4. The gradient method
5. Nonlinear neural networks
6. External learning algorithm for feedback controls
7. Internal learning algorithm for feedback controls
8. Learning processes of cognitive systems
9. Qualitative analysis of static problems
10. Dynamic qualitative cognitive systemsReadership: Researchers in neural networks and cognitive systems
The book covers three topics: (i) neural networks and the mathematical background needed to treat them, (ii) cognitive systems and (iii) mathematical issues in qualitative physics. The book is an excellent introduction to these topics from a more mathematical perspective. The book is strongly recommended to readers with a mathematical background who wish to gain an appreciation of the "hard science" side of neural networks or cognitive systems.
Reviewer: Institute The University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title MULTIVARIATE DEPENDENCIES: MODELS, ANALYSIS AND INTERPRETATION. Author D.R. Cox and N. Wermuth. Publisher London: Chapman and Hall, 1996, pp. xii + 255, £30.00. Contents:
1. Introduction
2. Aspects of interpretation
3. Technical considerations
4. Statistical analysis
5. Special methods for joint responses
6. Some specific applications
7. Some strategic aspects
8. Some more specialized topicsReadership: Research workers, especially in the applied social sciences; statisticians
Social scientists and their statistical advisors are often confronted with large sets of observational data and very little by way of background knowledge of statistical analysis. Particular techniques may be in the armoury: regression, path analysis, factor analysis. A variety of tools will be to hand in the form of statistical packages. What is missing is a coherent strategy for analysis, grounded in substantive knowledge and allowing later substantive interpretation of the results. This book provides the basis for such a strategy. Technical and interpretive issues are systematically developed and illustrated by numerous short examples and four substantial studies. A graph-theoretic notation is used to convey the structure of the models in a compact but precise way. The book is exceptionally well written, quite Mozartian in its elegance and economy of style. It does make assumptions about the background knowledge and seriousness of purpose of the reader and for this reason is not a book for beginners or amateurs. However researchers who are prepared to take the trouble to familiarize them-selves with the underlying statistical concepts will find it an invaluable companion in the analysis and interpretation of multivariate data.
Reviewer: Institute London School of Economics Place London, U.K. Name B. Farbey
Title BIPLOTS. Author J.C. Gower and D.J. Hand. Publisher London: Chapman and Hall, 1996, pp. xvi + 277, £,32.00. Contents:
1. Introduction
2. Principal components analysis (PCA)
3. Other linear biplots
4. Multiple correspondence analysis
5. Canonical biplots
6. Nonlinear biplots
7. Generalized biplots
8. Biadditive models
9. Correspondence analysis (CA)
10. Relationships between CA and MCA
11. Other topicsReadership: Experimental scientists, statisticians, postgraduate students of statistics
Biplots are introduced as "the multivariate analogue of scatter plots". Due originally to K.R. Gabriel and co-workers, the basic ideas have more recently been generalized by J.C. Gower. The bi-plot viewpoint provides an attractive and refreshing way of approaching many methods of multivariate analysis. This is especially true with regard to the distinction between interpolation and prediction. In prediction, when an object is displayed in a plot, the values of its variables are inferred, while in interpolation, the objects variables are known, and its position in the plot is required. In order to follow the material of this book it is necessary to have a good working know-ledge of linear algebra. The main results are found in a thirty page appendix, which is a most useful general reference. Understanding is helped by geometrical interpretations, and excellent detailed illustrations are provided throughout, using a variety of historical sets of data. This fascinating book is essential reading for all students of multivariate analysis. There is new work here, and enthusiastic readers can take up the challenge of further extending and implementing the material.
Reviewer: Institute University of Kent Place Canterbury, U.K. Name B.J.T. Morgan
Title AN INTRODUCTION TO CATEGORICAL DATA ANALYSIS. Author A. Agresti. Publisher New York: Wiley, 1996, pp. xi + 290, £24.95. Contents:
1. Introduction
2. Two-way contingency tables
3. Three-way contingency tables
4. Generalized linear models
5. Logistic regression
6. Loglinear models for contingency tables
7. Building and applying logit and loglinear models
8. Multicategory logit models
9. Models for matched pairs
10. A twentieth-century tour of categorical data analysisReadership: Applied statisticians, experimental scientists, students of statistics
This is a superb text from which to teach categorical data analysis, at a variety of levels. It is not overloaded with references, there are just two pages of these in the Bibliography, and the author emphasizes that much of the analysis can be carried out without a deep understanding. For example, computational details are omitted, in favour of how to program in SAS, and general discussion of maximum likelihood is deferred until page 195. Good illustrative examples recur throughout the book, and there is a wealth of problems at the end of each of the first nine chapters. A set of solutions would be useful, and might for ex-ample join the tables and sets of data from the book already available on the Word Wide Web and StatLib. The review of Chapter 10 places the work in its historical context, which leads naturally into the computing appendix, which focuses on SAS code, especially PROC GENMOD. This book can be very highly recommended.
Reviewer: Institute University of Kent Place Canterbury, U.K. Name B.J.T. Morgan
Title MULTIPLE COMPARISONS: THEORY AND METHODS. Author J.C. Hsu. Publisher New York: Chapman and Hall, 1996, pp. xiv + 277, £35.00. Contents:
1. Introduction to simultaneous statistical inference
2. Classification of multiple comparison methods
3. Multiple comparisons with control
4. Multiple comparisons with the best
5. All-pairwise comparisons
6. Abuses and misconceptions in multiple comparisons
7. Multiple comparisons in the general linear modelReadership: Data analysts, statisticians
The book contains excellent sections on motivation for simultaneous inference and on abuses and misconceptions in multiple comparisons. A careful discussion of error rates is included. The author draws a clear distinction between control of familywise error rates in the strong and weak senses. This distinction is important in recommendations for various methods. All methods are illustrated on interesting sets of data and software implementation is thoroughly discussed. Confident directions and confident inequalities are introduced as an alternative to traditional confidence intervals. The author has succeeded in presenting a highly readable account of the most up to date methodology. There is an extensive bibliography including fifty-seven entries from the 1990s alone.
Reviewer: Institute Pennsylvania State University Place University Park, U.S.A. Name T.P. Hettmansperger
Title PRACTICAL LONGITUDINAL DATA ANALYSIS. Author D.J. Hand and M. Crowder. Publisher London: Chapman and Hall, 1996, pp. x + 232, £35.00. Contents:
1. Introduction
PART I : Normal Error Distributions
2. Multivariate analysis of variance
3. Univariate analysis of variance
4. Regression methods
5. Random effects models
6. Covariance structures
Part II : Non-normal Error Distributions
7. Continuous non-normal measures: Gaussian estimation
8. Nonlinear models
9. Generalized linear models and maximum quasi- likelihood estimation
10. Binary and categorical measures
PART III: Comparisons of Methods
11. Relationships between methodsReadership: Academic, professional and consulting statisticians
Written in a lucid style, with occasional flashes of humour, the author discusses the analysis of longitudinal or repeated measurement data, from a regression viewpoint. As data of this type can often be analyzed in more than one way, the choice of method depends largely on assumptions about the structure of the covariance matrix. The various methods are compared and contrasted. Emphasis throughout is strongly on the implementation of the techniques and as such it complements their earlier book Analysis of Repeated Measures [Short Book Reviews, Vol. 10, p.45]. Illustrative examples are used instead of mathematical derivations. These examples elucidate the somewhat cryptic matrix formulations for longitudinal data that occur in the literature and also show how differences in the under-lying assumptions affect the results.
The book is divided into three parts. The first part dealing with well-established normal-theory models. In the examples, commercially available soft-ware, complete with code and output, is given. The second part of the book presents a timely review of the important methods developed over the past ten years for handling longitudinal, categorical or binary data. These methods rest largely on estimating equations and quasi-likelihood approaches. As there is no widely available commercial software for these methods, pro-grams written by the second author are used. This section of the book provides a valuable introduction to these methods. In the third part, the authors com-pare various methods. Two appendices contain sets of data which are available on the internet. All in all, this book is a welcome addition to the literature both for the data analyst and for those wishing to gain in-sight into a large and important branch of statistical theory. The book is highly recommended.
Reviewer: Institute University of Cape Town Place Rondebosch, South Africa Name J.M. Juritz
Title PRACTICAL SAMPLING TECHNIQUES, 2nd edition, Revised and expanded. Author R.K. Som. Publisher New York: Dekker, 1996, pp. xxix + 635. Contents:
1. Basic concepts of sampling
PART I : Single-Stage Sampling
2. Simple random sampling
3. Ratio and regression estimators
4. Systematic sampling
5. Varying probability sampling: Sampling with probability proportional to size
6. Choice of sampling units: Cluster sampling
7. Size of sample: Cost and error
8. Self-weighting designs
PART II : Stratified Single-Stage Sampling
9. Stratified sampling: Introduction
10. Stratified simple random sampling
11. Stratified varying sampling
12. Size of sample and allocation to different strata
13. Self-weighting designs in stratified single-stage sampling
PART III: Multi-Stage Sampling
14. Multi-stage sampling: Introduction
15. Multi-stage simple random sampling
16. Multi-stage varying probability sampling
17. Size of sample and allocation to different stages
18. Self-weighting designs in multi-stage sampling
PART IV : Stratified Multi-Stage Sampling
19. Stratified multi-stage sampling: Introduction
20. Stratified multi-stage simple random sampling
21. Stratified multi-stage varying probability sampling
22. Size of sample and allocation to different strata and stages
23. Self-weighting designs in stratified multi-stage sampling
PART V : Miscellaneous Topics
24. Miscellaneous sampling topics
25. Errors and biases in data and estimates
26. Planning, execution and analysis of surveys
27. The use of personal computers in survey samplingReadership: Sample survey practitioners
This is the second edition of a book first published in 1973 as A Manual of Sampling Techniques. After an introductory chapter in which most of the terminology and concepts are defined, the book is divided into five parts: the first four cover, in considerable detail, single-stage and multi-stage sampling with and without stratification: the final part discusses a variety of more specialized topics such as the jackknife and bootstrap methods. The text presents a logical and clear account of the practical ideas involved in planning and executing a sample survey. The reasons for using different sampling methods, (simple, systematic, varying probability, stratified, etc.), and different estimating procedures, (mean, ratio and regression), are discussed in detail. Numerous examples using data from actual large-scale sample surveys in Europe, the United States, Asia and Africa are provided to illustrate the methods. Exercises, some with solutions, are given at the end of each chapter. Theoretical development is kept to a minimum in the main sections, but an appendix of more than twenty pages of proofs of some of the main results is included. With nearly thirty pages of references, this is an excellent manual which, with some selection, could easily be used as course text.
Reviewer: Institute University of Southampton Place Southampton, U.K. Name P. Prescott
Title LOCAL POLYNOMIAL MODELLING AND ITS APPLICATIONS. Author J. Fan and I. Gijbels. Publisher London: Chapman and Hall, 1996, pp. xv + 341, £35.00. Contents:
1. Introduction
2. Overview of existing methods
3. Framework for local polynomial regression
4. Automatic determination of model complexity
5. Applications of local polynomial modelling
6. Applications in nonlinear time series
7. Local polynomial regression for multivariate dataReadership: Research and applied statisticians
This is an ambitious book which seeks to present an up-to-date account of the vast subject of nonparametric regression techniques. The authors succeed in making the material accessible to a large potential readership of researchers and practitioners by using a judicious balance of theory and practice. The book is certainly right up-to-date, including subjects such as wavelet thresholding and sliced inverse regression. The use of sections at the end of the main chapters to contain more technical arguments, and to give bibliographic notes works well and helps to un-clutter the main text. The text assumes a wide know-ledge of the nomenclature of the subject. Sometimes brief additional explanation might have been useful. For example, Section 2.5.2 mentions the `extremal phase family' of wavelet filters; here it could have been pointed out that such filters generate invertible models in Box and Jenkins time series terminology. One annoying feature of the book is the lack of labelling of the axes of many of the graphs; this is surely a basic scientific requirement and should be corrected in future editions. However, overall I would highly recommend this book to all statisticians, all of whom are likely to use one or more of the methods discussed in this comprehensive book.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name A.T. Walden
Title MONTE CARLO. CONCEPTS, ALGORITHMS, AND APPLICATIONS. Author G.S. Fishman. Publisher New York: Springer-Verlag, 1996, pp. xxv + 698, US$69.00. Contents:
1. Introduction
2. Estimating volume and count
3. Generating samples
4. Increasing efficiency
5. Random tours
6. Designing and analyzing sample paths
7. Generating pseudorandom numbersReadership: Graduate and advanced undergraduate students in the mathematical and engineering sciences; reference material for operations researchers and statisticians who use Monte Carlo methods
This thick, nine-inch by seven-inch wide volume in the Springer Series in Operation Research has considerable heft and made a good impression on me at the outset! The early Roman-numbered pages contain the usual table of contents and also "Selected Notation" lists for Chapters 2 to 7, which is very nice indeed. A well-written introductory Chapter 1 includes some suggestions of how various audiences can read the book, and how to ftp a copy of FORTRAN software from the University of North Carolina.
Chapters 2 to 7 are all long ones. The writing style is "no nonsense, this is the way it's done". In the sub-sections on statistical distributions in Chapter 3, we find indications of the best ways to generate samples, and outlines which set out, in self-contained manner, the algorithms suggested. Overall, the text shows logical organization and careful writing and is beautifully produced. This is an impressive and useful book for a wide readership. Libraries should order this immediately.
Reviewer: Institute University of Wisconsin Place Madison, U.S.A. Name N.R. Draper
Title A GUIDE TO CHI-SQUARED TESTING. P.E. Greenwood and Author M.S. Nikulin. Publisher New York: Wiley, 1996, pp. xii + 280, £29.95. Contents:
1. The chi-squared test of Pearson
2. The chi-squared test for a composite hypothesis
3. The chi-squared test for an exponential family of distributions
4. Some additional examplesReadership: Experimental scientist with a basic knowledge of statistics, consultant statistician
This volume attempts to update H.O. Lancaster's (1969) Chi-squared Distribution whilst recognizing that the extent of the subject today means that many readers may also need to consult Reed and Cressie's (1988) Goodness-of-Fit Statistics for Discrete Multivariate Data, [Short Book Reviews, Vol. 9, p.25], Rayner and Best's (1989) Smooth Tests of Good-ness-of-Fit, and possibly Drost's (1988) Asymptotics for Generalized Chi-squared Goodness-of-Fit Tests, [Short Book Reviews, Vol. 8, p.43]. Each of these books reflects its authors' particular interests. Greenwood and Nikulin emphasize the proper use of chi-squared tests in standard hypothesis-testing situations.
Strengths of the book include the consideration of other tests that are asymptotically chi-squared, the effect of applying a chi-squared test to data from which parameter estimates have already been made, and how and when to group data. An experimental scientist with only a basic knowledge of statistics could find the mathematical treatment heavy-going in places; the text and the recommendations are clearly presented however. Consultant statisticians might prefer the distributional coverage of the examples to match more closely the distributions that are in frequent use by their clients. Nevertheless, this is a useful addition to the literature on chi-squared tests and is particularly valuable for the window that it opens on to the research in the former Soviet Union.
Reviewer: Institute St. Andrews University Place St. Andrews, U.K. Name A.W. Kemp
Title ROBUST STATISTICAL PROCEDURES. Asymptotics and Interrelations. Author J. Jurecková and P.K. Sen. Publisher New York: Wiley, 1996, pp. xiv + 466. Contents:
1. Introduction and Synopsis
PART I : Asymptotics and Interrelations
2. Preliminaries
3. Robust estimation of location and regression
4. Asymptotic representations of L-estimators
5. Asymptotic representations of M-estimators
6. Asymptotic representations of R-estimators
7. Asymptotic interrelations of estimators
PART II: Robust Statistical Inference
8. Robust sequential and recursive point estimation
9. Robust confidence sets and intervals
10. Robust statistical testsReadership: Graduate students and researchers in mathematical statistics
Every statisticians is aware of the fact that a statistical procedure may be very sensitive to departures from the assumptions of the underlying model. This is only one aspect of what nowadays is dealt with in robust statistics. This book is a specialized treatment on the theoretical background of robustness of statistical procedures. It provides, in a unified way, the asymptotic representation theory for the classical L-, M-, and R-statistics in the framework of a location or regression model. Also theory is presented for other statistics like differentiable statistical functionals, regression quantiles, etc. The focus is on asymptotic theory and the interrelations between the various classes of statistics (Part I) as well as on robust statistical inference (Part II). The treatment is mathematical in the format: conditions, theorem, proof of the theorem. At the end of each chapter there is a section with problems. In total there are more than two-hundred exercises, although some of them are of the less inviting type "Verify formula (.)". The book is an invaluable instrument for researchers in the field of robustness. The five-hundred items in the bibliography (of which more than one hundred and fifty are by the authors of the book) are a most valuable reference source.
Reviewer: Institute Limburgs Universitair Centrum Place Diepenbeek, Belgium Name N. Veraverbeke
Title MARKOV CHAIN MONTE CARLO IN PRACTICE. Author W.R. Gilks, S. Richardson and D.J. Spiegelhalter (Eds.). Publisher London: Chapman and Hall, 1996, pp. xvii + 486, £.00. Contents:
1. Introducing Markov chain Monte Carlo, by W.R. Gilks, S. Richardson and D.J. Spiegelhalter
2. Hepatitis B: A case study in MCMC methods, by D.J. Spiegelhalter, N.G. Best, W.R. Gilks and H. Inskip
3. Markov chain concepts related to sampling algorithms, by G.O. Roberts
4. Introduction to general state-space Markov chain theory, by L. Tierney
5. Full conditional distributions, by W.R. Gilks
6. Strategies for improving MCMC, by W.R. Gilks and G.O. Roberts
7. Implementing MCMC, by A.E. Raferty and S.M. Lewis
8. Inference and monitoring convergence, by A. Gelman
9. Model determination using sampling-based methods, by A.E. Gelfand
10. Hypothesis testing and model selection, by A.E. Raftery
11. Model checking and model improvement, by A. Gelman and X.-L. Meng
12. Stochastic search variable selection, by E.I. George and R.E. McCulloch
13. Bayesian model comparison via jump diffusions, by D.B. Phillips and A.F.M. Smith
14. Estimation and optimization of functions, by C.J. Geyer
15. Stochastic EM: Method and applications, by J. Diebolt and E.H.S. Ip
16. Generalized linear mixed models, by D.G. Clayton
17. Hierarchical longitudinal modelling, by B.P. Carlin
18. Medical monitoring, by C. Berzuini
19. MCMC for nonlinear hierarchical models, by J.E. Bennett, A. Racine-Poon and J.C. Wakefield
20. Bayesian mapping of disease, by A. Mollié
21. MCMC in image analysis, by P.J. Green
22. Measurement error, by S. Richardson
23. Gibbs sampling methods in genetics, by D.C. Thomas and W.J. Gauderman
24. Mixtures of distributions: Inference and estimation, by C.P. Robert
25. An archaeological example: Radiocarbon dating, by C. Litton and C. BuckReadership: Applied statisticians, biostatisticians and statistically-oriented epidemiologists and computer scientists
Originating from statistical physics, Markov chain Monte Carlo (MCMC) techniques are becoming increasingly important in various fields of statistics. Its main applicability concerns high-dimensional integration as for instance typically encountered in Bayesian analysis and imaging. The basic idea is to approximate an expectation of a function of a random vector X with respect to a measure TT by a discrete average where the discrete skeleton is constructed via an appropriate Markov chain with stationary distribution TT. An ergodic theorem should prove convergence of the approximation. This edited volume (twenty-five contributions from thirty-two authors) gives a very readable survey of the basic theory, the practical implementation as well as various examples. The latter, though mainly from the field of biostatistics, nevertheless give the reader a good idea of the usefulness of MCMC in much more general models. This volume will definitely be instrumental in making MCMC known to a wider audience of statisticians.
Reviewer: Institute ETH-Zürich Place Zürich, Switzerland Name P.A.L. Embrechts
Title RANDOM SUMMATION. LIMIT THEOREMS AND APPLICATIONS. Author B. V. Gnedenko and V.Y. Korolev. Publisher Boca Raton, Florida: CRC Press, 1996, pp. viii + 267, US$79.95. Contents:
1. Examples
2. Doubling with repair
3. Limit theorems for "growing" random sums
4. Limit theorems for random sums in the double array scheme
5. Mathematical theory of reliability growth. A Bayesian approachReadership: Applied probabilists, reliability engineers
The "random summation" in the title refers to the summation of a random number N of independent and identically distributed random variables. Though not necessary, the latter variables are taken to be positive and independence between N and the sequence of summands is mostly assumed. Motivating examples mainly come from queuing theory, reliability engineering and insurance risk theory. Main emphasis, is given to limit theory. The examples mostly contain reformulations of the general results to several special cases. The book yields an interesting summary of the recent mainly Russian contributions to this important area of applied research. The language sounds rather artificial throughout: as with so many books these days, language editing by the publishers would have considerably improved the final outcome. All in all, a useful book for the (applied) specialist working with such random summation models.
Reviewer: Institute ETH-Zürich Place Zürich, Switzerland Name P.A.L. Embrechts
Title RANDOM WALKS AND RANDOM ENVIRONMENTS. Volume 2: Random Environments. Author B.D. Hughes. Publisher Oxford: Clarendon Press, 1996, pp. xxiv + 526, £55.00. Contents:
1. An introduction to percolation theory
2. Bernoulli site percolation
3. Percolation thresholds
4. Critical exponents in percolation theory
5. Transport and conduction in random environments
6. Random walk in a random environment
7. The ant in the labyrinthReadership: Probabilists, statistical physicists
Volume 1 [Short Book Reviews, Vol. 15, p.4.] is devoted to the theory of random walks, i.e. to the case when the space is deterministic and homogeneous and the moving particle chooses random directions. In the present volume the random disorder is "frozen" in the space. The most typical example of this phenomena is percolation when the sites or bonds are open or closed with a given probability 0
Reviewer: Institute Technische Universität Place Wien, Austria Name P. Révész
Title STOCHASTIC PROCESSES: GENERAL THEORY. Author M.M. Rao. Publisher Dordrecht, The Netherlands: Kluwer, 1995, pp. xii + 623, Dfl.360.00/US$259.00/,159.00. Contents:
PART I : Introduction and Foundations
PART II : Conditioning and Martingales
PART III: Stochastic Function Theory
PART IV : Refinements in Martingale Analysis
PART V : Martingale Decompositions and Integration
PART VI : Stochastic Integrals and Differential Systems
PART VII: Stochastic Analysis on Differentia Structures lReadership: Researchers and graduate students in probability
This new edition of the 1979 "Stochastic Processes and Integration" is completely reworked. The author gives a very concise and self-contained treatment on the general theory of processes. In it, the reader will not explicitly find special processes like for instance Poisson or renewal processes, but is offered a detailed discussion on the basic construction and properties of stochastic processes, continuous time (semi-) martingales and stochastic integrals based on such processes. The key tool (and indeed novelty) in the latter construction is Bochner's boundedness principle. From a mathematical point of view, the text offers a very sound and readable treatment of the foundations and key results. The exercises are mostly very taxing containing occasionally results which in many other textbooks would appear as new theory. One of the key features of the general theory of processes is its surprising applicability to diverse fields. Examples of this are not discussed. On the other hand, I found the book competently and scholarly written. As such, the (mathematically mature) post graduate student will find a lot of important material in it. I, there-fore, recommend it for that readership.
Reviewer: Institute ETH-Zürich Place Zürich, Switzerland Name P.A.L. Embrechts
Title MODELS OF RANDOM PROCESSES. A Handbook for Mathematicians and Engineers. Author I.N. Kovalenko, N.Y. Kuznetsov and V.M. Shurenkov. Publisher Boca Raton, Florida: CRC Press, pp. 446. Contents:
Introduction
1. Definitions and general properties of random processors
2. Classification of random processors
3. Discrete-time Markov chains
4. Main classes of constructively defined random processes
5. Random processes with independent increments
6. Processes associated with a Poisson process
7. Random flows and events
8. Classes of constructively defined random processes
9. Some special classes of processes
10. Stability of random processes
11. Random processes of statistical radio engineering
12. Renewal theory
13. Branching processes
14. Ergodic theory and stationary processes
15. Markov processes
16. Statistics for some classes of random processes
17. Simulation of random processesReadership: Engineers and statisticians who are involved in the modelling of physical phenomena
This handbook is an updated version of a 1983 Russian edition. It gives a comprehensive survey of random processes that can be used to model different types of physical phenomena. All necessary background is provided. The book covers three areas: (i) general theory, (ii) processes arising from applications and (iii) special random process needed in special situations. Typically the proofs of various results are left to the extensive background references. The book would be a valuable resource for somebody who wants to know how to get started in the modelling of a particular kind of physical phenomena involving random effects.
Reviewer: Institute The University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title PROBABILITY MEASURES ON SEMIGROUPS. Convolution Products, Random Walks, and Random Matrices. Author G. Högnäs and A. Mukherjea. Publisher New York: Plenum Press, 1995, pp. xii + 388, US$89.50. Contents:
1. Semigroups
2. Probability measures on topological semigroups
3. Random walks on semigroups
4. Random matricesReadership: Graduate students and other researchers, particularly mathematicians, physicists, computer scientists
This is a well-written book. Its subject matter is outside my usual field of interest and an initial scan through left me feeling that this review was going to involve some work. When I finally found time to take a considered look, I was surprised and pleased. This is elegant mathematics, motivated by examples and presented in an accessible way that engages the reader.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name C. Barnett
Title NONPARAMETRIC STATISTICS FOR STOCHASTIC PROCESSES. Estimation and Prediction. Author D. Bosq. Publisher New York: Springer-Verlag, 1996, pp. xii + 169, US$39.95. Contents:
Synopsis
1. Inequalities for mixing processes
2. Density estimation for discrete time processes
3. Regression estimation and prediction for discrete time processes
4. Density estimation for continuous time processes
5. Regression estimation and prediction in continuous timeReadership: Researchers and specialists in mathematical statistics, stochastic processes and time series analysis
This is a well-balanced book written at a mathematically high level which deals essentially with nonparametric density estimation and regression estimation in both discrete and continuous cases. The book begins by a synopsis where basic notions as kernel density estimator, kernel regression estimator and mixing processes are introduced. In this last case the author introduces the strong mixing coefficient. Techniques of density estimation for discrete time processes presented achieve the optimal rates, that is the same rates as in the independent and identically distributed case. For the continuous case as well as for regression estimation and prediction the results obtained enjoy the "superoptimal rate". Most of the results presented for continuous time processes are new. The Appendix consists of several numerical results comparing performances of nonparametric predictors and parametric predictors (Box-Jenkins) using two criteria. In each case the nonparametric predictor clearly out-beats his parametric competitor. Two real sets of data concerning car registrations and electricity consumption are analyzed. In short, this is a compelling book which combine mathematically rigorous developments of the theory of nonparametric estimation and prediction for stochastic processes and numerical applications.
Reviewer: Institute Université de Sherbrooke Place Sherbrooke, Canada Name E. Monga
Title WHITE NOISE DISTRIBUTION THEORY. Author H.-H. Kuo. Publisher Boca Raton, Florida: CRC Press, 1996, pp. ix + 378, US$69.95. Contents:
1. Introduction to white noise
2. Background
3. White noise as an infinite dimensional calculus
4. Constructions of test and generalized functions
5. The S-transform
6. Continuous versions and analytic extensions
7. Delta functions
8. Characterizations theorems
9. Differential operators
10. Integral kernel operators
11. Fourier transforms
12. Laplacian operators
13. White noise integration
14. Feynnman integrals
15. Positive generalized functionsReadership: Probabilists, analysts
A theory of white noise as the derivative of the Brownian motion process is developed. This is done through an extension of Laurent Schwartz's distribution (generalized function) theory to infinite dimensional spaces. The theory grows out of Hida's theory of white noise. The author says that the "book is accessible to anyone with a first year graduate course in real analysis and some knowledge of Hilbert spaces." Some know-ledge of topological vector spaces and of Schwartz's distribution theory would also be helpful. The book will be difficult reading for many who use rather informal definitions of white noise in applications, but a careful reading should reassure users of these definitions that a more rigorous foundation can be provided for their calculations.
Reviewer: Institute Queen's University Place Kingston, Canada Name L.L. Campbell
Title NUMERICAL BAYESIAN METHODS APPLIED TO SIGNAL PROCESSING. Author J.J.K. O'Ruanaidh and W.J. Fitzgerald. Publisher New York: Springer-Verlag, 1996, pp. xiv + 244, US$49.95. Contents:
1. Introduction
2. Probabilistic inference in signal processing
3. Numerical Bayesian inference
4. Markov chain Monte Carlo methods
5. Retrospective changepoint detection
6. Restoration of missing samples in digital audio signals
7. Integration in Bayesian data analysis
8. ConclusionReadership: Engineers with an interest in digital signal processing
This book discusses the application of Bayesian methods to the core problems of signal pro-cessing. Although Bayesian methods are often viewed with suspicion they are a powerful tool in real problems wherein the prior probability can be viewed as a regularization technique. This book discusses three different aspects of Bayesian inference, namely optimization (maximizing a density function) integration (finding marginal densities) and simulation (finding typical random vectors from a density). The book gives a simple and clear introduction to these ideas within a Bayesian framework with emphasis on computational procedures for problems having no fixed form solution.
Reviewer: Institute The University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title THE NORMAL DISTRIBUTIONCCCHARACTERIZATIONS AND APPLICATIONS. Author W. Bryc. Publisher New York: Springer-Verlag, 1995, pp. viii + 139, DM.68.00/ÖS.530.40/Sw.fr.65.50. Contents:
1. Probability tools
2. Normal distributions
3. Equidistributed linear forms
4. Rotation invariant distributions
5. Independent linear forms
6. Stability and weak stability
7. Conditional moments
8. Gaussian processesReadership: Probabilists
Characterizations of distributions are intrinsically interesting: they are usually based on elementary properties of a distribution, they are easy to state, they can be understood by a wide audience, they surgically delineate the family of distribution functions, they have important practical applications, and they are frequently extremely difficult to establish often resting on ingenious arguments. This compact account of the special case of the normal distribution has a most engaging introduction with a quotation from the 19th century astronomer, J.F.W. Herschel, who gave one of the early characterizations based on rotational symmetry, one which is developed extensively later in the book. Most of the standard characterizations appear at some point and a number are then used to provide competing definitions of Gaussian random vectors in abstract spaces, all of which reduce to the standard multivariate normal when the space in question is Euclidean n-space. Zero-one laws are derived for these abstract spaces with the relevant events being member-ship of linear subspaces. This is designed in part as a graduate course and includes sets of problems. The material is very well motivated, explanations are clear. The book sets recent work in context and re-presents a valuable addition to the standard texts on characterizations.
Reviewer: Institute Macquarie University Place Sydney, Australia Name J.R. Leslie
Title ALGORITHMIC PROBABILITY. A COLLECTION OF PROBLEMS. Author M.F. Neuts. Publisher London: Chapman and Hall, 1995, pp. xii + 465, £35.00. Contents:
1. Computational probability: An introduction
2. Solving equations
3. Functions of random variables
4. Discrete-time Markov chains
5. Continuous-time Markov chains
6. Experimentation and visualization
APPENDIX 1: Some Topics from Matrix Algebra
APPENDIX 2: Phase-Type Distributions
APPENDIX 3: The Markovian Arrival ProcessReadership: Applied probabilists, teachers of applied probability, engineers and operations analysts, and advanced students of engineering, technology and computing
Algorithmic probability is the name that the author gives to an exploratory probability that will generally require computer experimentation. Here we have a collection of more than four hundred challenging problems. These are often taken from engineering applications of stochastic modelling. The solver is given a structured path to follow: expand this, show that, write a program to compute this, print the probabilities for that. Sixty-five of the problems are given outline solutions, and for many others references are given. The preface describes the problems as being elementary but complex, and asks that the solvers have taken at least introductory courses at the advanced undergraduate or beginning graduate level. We should be grateful that a distinguished professor of systems and industrial engineering has made his collection of problems and projects available to all. It is possible to criticize the writing which is unpolished, and the printing which is often smudgy, and I do hate being ordered about C do this, do that C but students, if not their teachers, will be used to that.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name R. Coleman
Title AN INTERMEDIATE COURSE IN PROBABILITY. Author A. Gut. Publisher New York: Springer-Verlag, 1995, pp. xiii + 278, DM.48.00/ÖS.350.40/Sw.fr.48.00. Contents:
Introduction
1. Multivariate random variables
2. Conditioning
3. Transforms
4. Order statistics
5. The multivariate normal distribution
6. Convergence
7. The Poisson processReadership: Students having taken a first undergraduate course in probability
"Intermediate" in the title stands for a level between the first undergraduate course in probability and the first graduate one. The latter can be on stochastic processes or a measure theoretic probability course. For both types of courses, this book offers a very readable preparation. It gives a nice balance between analytic and probabilistic techniques. The various examples and exercises make it also interesting for self study. A long chapter, fifty pages, on the Poisson process provides an ideal transition to the theory of stochastic processes.
Reviewer: Institute ETH-Zürich Place Zürich, Switzerland Name P.A.L. Embrechts
Title MODELING AND ANALYSIS OF STOCHASTIC SYSTEMS. Author V.G. Kulkarni. Publisher London: Chapman and Hall, 1995, pp. xi + 619, £49.99. Contents:
1. Introduction
2. Discrete-time Markov chains: Transient behaviour
3. Discrete-time Markov chains: Limiting behaviour
4. Discrete-time Markov chains: First passage times
5. Poisson processes
6. Continuous-time Markov chains
7. Applications of Markov chains to queueing theory
8. Renewal processes
9. Markov renewal processesReadership: Final-year undergraduate statistics majors, graduates with knowledge of advanced calculus and some matrix theory
This is a classical, non-measure-theoretic approach to discrete state space stochastic processes designed for graduate students in "operations research, computer science, business and public policy analysis (and) engineering" although a wider audience including final year maths/statistics undergraduates would find it useful. Roughly speaking, it is after the style of Karlin and Taylor. The theoretical material in the book is presented in bite-sized quantities and these are followed by a generous supply of worked examples. There are plenty of exercises and they are classified as "modelling" (not involving analysis), "computation" (may require numerical and/or algebraic manipulation) and "conceptual" (proving theorems). The classification is evidently intended to help lecturers set balanced assignments. Explanations are clear and the modelling exercises should help students to recognize and identify discrete state processes when they encounter them in the outside world. There is also a useful discussion of the standard algorithms used in finding stationary distributions numerically.
One thing that is missing in texts such as this is a collection of case studies in which important and interesting real-world problems have been solved or have had useful light shed on them by the sorts of analyses that are the subject of the book. If stochastic process theory is so important to business students, to public policy analysts and to engineers that it is worth their while undertaking a course such as this then there must by now be many interesting, in a popular sense, problems that have been usefully analyzed by these methods and where the analysis has made a difference to the outcomes. Whilst the author took considerable care to emphasize the practical relevance of the various processes it is the immediacy, the spontaneous interest of real data, real people and real problems that are missing. Issues such as the estimation of parameters can be glossed over at this level.
Reviewer: Institute Macquarie University Place Sydney, Australia Name J.R. Leslie
Title MARKOV PROCESSES AND DIFFERENTIAL EQUATIONS: ASYMPTOTIC PROBLEMS. Author M. Freidlin. Publisher Basel: Birkhäuser, 1996, pp. 152, DM. 44.00/ÖS.321.20/Sw.fr.38.00. Contents:
1. Stochastic processes defined by ODE's
2. Small parameter in higher derivatives: Levinson's case
3. The large deviation case
4. Averaging principle for stochastic processes and for partial differential equations
5. Averaging principle: Continuation
6. Remarks and generalizations
7. Diffusion processes and PDE's in narrow branching tubes
8. Wave fronts in reaction-diffusion equations
9. Wave fronts in slowly changing media
10. Large scale approximation from reaction-diffusion equations
11. Homogenization in PDE's and in stochastic processesReadership: Advanced students and researchers in probability and partial differential equations
This monograph uses Markov process formulations to address asymptotic topics arising from partial differential equations. These topics, indicated in the titles of the book's several chapters, have been the focus of much research by the author. The main theme is the use of probabilistic limit theorems and large deviation theory to solve problems in these several areas that concern random perturbations of dynamical systems, homogenization and wave front propagation. The material is well presented and current, making this brief monograph a worthwhile addition to the literature of stochastic PDE's.
Reviewer: Institute University of Washington Place Seattle, USA Name R. Pyke
Title WEAK CONVERGENCE AND EMPIRICAL PROCESSES. WITH APPLICATIONS TO STATISTICS. Author A.W. van der Vaart and J.A. Wellner. Publisher New York: Springer-Vrlag, 1996, pp. xvi + 508, US$44.95. Contents:
1. Stochastic convergence
2. Empirical processes
3. Statistical applicationsReadership: Probabilists and statisticians
Based on the ideas of J. Hoffman-Jorgensen and R.M. Dudley, Part 1 of the book, Stochastic Convergence, gives an exposition of a general theory of weak convergence, which accommodates random elements that are not necessarily Borel measurable. Such a theory has evolved mainly in developing the asymptotic theory of empirical processes indexed by classes of sets and functions that, in turn, is studied in Part 2 of the book, Empirical Processes. The aim of Part 2 is to make this theory more accessible to statisticians as well as to probabilists interested in statistical applications. Part 3, Statistical Applications, is devoted to illustrate the usefulness of these theoretical developments for statistics by a wide variety of applications that range from rates of convergence in semiparametric estimation, to the functional delta-method, bootstrap permutation empirical processes and the convolution theorem. The appendix covers a number of auxiliary subjects that are used to develop some of the material in the three main Parts. The material presented in these three parts is meant to be self-contained to a reasonable extent.
Reviewer: Institute Carleton University Place Ottawa, Canada Name M. Csörgö
Title CONTROL OF UNCERTAIN SAMPLED-DATA SYSTEMS. Author G.E. Dullerud. Publisher Boston: Birkhäuser, 1996, pp. xiv + 177, DM.78.00/ÖS.569.40/ Sw.fr.68.00. Contents:
1. Introduction
2. Preliminaries
3. Uncertain sampled-data systems
4. Analysis of LTI uncertainty
5. A computational framework
6. Robustness performanceReadership: Control theorists, postgraduate students in control
A sampled-data system is a system in which continuous time and discrete time elements are mixed, as in computer control of a continuous time dynamical system. The book is concerned with the design of sampled-data systems in the presence of model un-certainty. Specifically, tools are presented allowing the analysis of the effects of structured uncertainty on the stabilization and performance of sampled-data systems. The book is a research monograph and is recommended to anybody with an interest in digital control of continuous time dynamic systems.
Reviewer: Institute The University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title MEASUREMENT ERROR IN NONLINEAR MODELS. R.J. Carroll, Author D. Ruppert and L.A. Stefanski. Publisher London: Chapman and Hall, 1995, pp. xxiv + 305, £29.95. Contents:
1. Introduction
2. Regression and attenuation
3. Regression calibration
4. Simulation extrapolation
5. Instrumental variables
6. Functional methods
7. Likelihood and quasilikelihood
8. Bayesian methods
9. Semiparametric methods
10. Unknown link functions
11. Hypothesis testing
12. Density estimation and nonparametric regression
13. Response variable error
14. Other topics
APPENDIX A: Fitting Methods and ModelsReadership: Scientists and statisticians with special interest in various types of nonlinear models when errors occur in the predictors
This research monograph on analyzing data using nonlinear models when there are errors in the predictors is a welcome addition to the bookshelf. Non-linear is widely interpreted here to include generalized linear models, transform-both-sides models, and quasilikelihood and variance function problems. Readers left behind in the outpouring of research on this topic in the last fifteen years will be grateful for this "snapshot of the current state of knowledge". The required prior knowledge for full comprehension is covered in Appendix A. However, the "Generalized Linear Models" Section (A.5) is a mere half page, because the authors defer to the well-known 1989 second edition of P. McCullagh and J.A. Nelder's book with that title [Short Book Reviews, Vol.10, p.6]. This present book is an essential purchase for the library and an excellent purchase for individuals.
Reviewer: Institute University of Wisconsin Place Madison, U.S.A. Name N.R. Draper
Title BAYESIAN DATA ANALYSIS. Author A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin. Publisher London: Chapman and Hall, 1995, pp. xix + 526, £29.95. Contents:
PART I : Fundamentals of Bayesian Inference
1. Background
2. Single-parameter models
3. Introduction to multiparameter models
4. Large sample inference and connections to standard statistical methods
PART II : Fundamentals of Bayesian Data Analysis
5. Hierarchical models
6. Model checking and sensitivity analysis
7. Study design in Bayesian analysis
8. Introduction to regression models
PART III: Advanced Computation
9. Approximations based on posterior modes
10. Posterior simulation and integration
11. Markov chain simulation
PART IV : Specific Models
12. Models for robust inference and sensitivity analysis
13. Hierarchical linear models
14. Generalised linear models
15. Multivariate models
16. Mixture models
17. Models for missing data
18. Concluding advice
APPENDIX A: Standard Probability Distributions
APPENDIX B: Outline of Proofs of Asymptotic TheoremsReadership: Graduate students, statisticians
The appeal of modern Bayesian analysis is its flexibility brought about by advances in computation. One of the strengths of this book is its coverage of computation. Two of its weaknesses are the range and level of involvement in its examples of data. Overall though it will certainly form a welcome addition to my limited but growing Bayesian library.
Reviewer: Institute University of Kent Place Canterbury, U.K. Name P.J. Brown
Title METHODS FOR UNCERTAINTY IN EDUCATIONAL TESTING. Author N.T. Longford. Publisher New York: Springer-Verlag, 1995, pp. xiv + 285, US$39.95. Contents:
1. Inference about variation
2. Reliability of essay rating
3. Adjusting subjectively rated scores
4. Rating several essays
5. Summarizing item-level properties
6. Equating and equivalence of tests
7. Inference from surveys with complex sampling design
8. Small-area estimation
9. Cut scores for pass/fail decisions
10. Incomplete longitudinal dataReadership: Psychometricians, educational researchers, statisticians
This is a collection of essays on a sample of what the author calls a "treasure trove of interesting statistical problems" encountered in his work at Educational Testing Service. He aims to bring modern statistical tools to sometimes old educational problems, such as the analysis of rating of essays and other constructed response measures. He also wants to remind educational researchers that similar problems are en-countered in other fields, and that much can be gained by pooling wisdom across application areas. His technique of choice is empirical Bayes or variance components modeling. The statistical level is rather sophisticated by the standards of education research journals, and the volume should interest research statisticians seeking new, interesting and important problems.
Reviewer: Institute McGill University Place Montreal, Canada Name J.O. Ramsay
Title TEST EQUATING: METHODS AND PRACTICES. Author M.J. Kolen and R.L. Brennen. Publisher New York: Springer-Verlag, 1995, pp. xviii + 333, US$44.95. Contents:
1. Introduction and concepts
2. Observed score equating using the random groups design
3. Random groups - Smoothing in equipercentile equating
4. Nonequivalent groups - Linear methods
5. Nonequivalent groups - Equipercentile methods
6. Item response theory methods
7. Standard errors of equating
8. Practical issues in equating and scaling to achieve comparabilityReadership: Psychometricians, test developers
Administration of a test on more than one occasion requires that multiple forms be developed and that they be scored so that scores on different forms can be regarded as equivalent or interchangeable. Test equating is the collection of statistical and other procedures by which reasonably equivalent scores can be constructed. Forms must necessarily be treated sym-metrically, and this rules out standard regression methods. Statistical equating methods can involve either linear or nonlinear transformations of raw form sources, and can also appeal to the notion of a true score and to the concept of a latent variable. This book is the first comprehensive monograph treating the extensive literature on both practical and statistical issues in equating, and the last chapter is essential reading for those facing an actual equating problem.
Reviewer: Institute McGill University Place Montreal, Canada Name J.O. Ramsay
Title METHODS OF MULTIVARIATE ANALYSIS. Author A.C. Rencher. Publisher New York: Wiley, 1995, pp. xvi + 627 + disk, ,58.00. Contents:
1. Introduction
2. Matrix algebra
3. Characterizing and displaying multivariate data
4. The multivariate normal distribution
5. Tests on one or two vectors
6. Multivariate analysis of variance
7. Tests on covariance matrices
8. Discriminant analysis: Description of group separation
9. Classification analysis: Allocation of observations to groups
10. Multivariate regression
11. Canonical correlation
12. Principal component analysis
13. Factor analysisReadership: Statisticians, students, scientists, social scientists
This is the first volume of a two-volume set, but the novelty is that the two volumes are not in-tended to be sequential. This first volume concentrates on methods, examples and actual data sets but omits many proofs of results; the second volume will include these proofs, emphasize derivations and algebraic exercises, and introduce additional topics.
The present volume is stronger on hypothesis testing than on descriptive or exploratory analyses. For example, MANOVA and associated ramifications receive a very full treatment but there is no mention of multidimensional scaling, correspondence analysis or cluster analysis. Also, most of the treatment is classical, with only eighteen of the two hundred and eighteen references being post-1985. However, we are promised that these drawbacks will be put right in the second volume.
Good features include the many sets of data and practical illustrations, and the full answers to exercises. A diskette is also provided, containing all the sets of data and SAS command files for the examples. While the aim of concentrating on necessary methodology is generally achieved, potential readers should be warned that quite a large amount of matrix algebra still survives. The total cost of the two-volume work is also a formidable prospect!
Reviewer: Institute University of Exeter Place Exeter, U.K. Name W.J. Krzanowski
Title NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. Author M. Davidian and D.M. Giltinan. Publisher London: Chapman and Hall, 1995, pp. xv + 359, £32.00. Contents:
1. Introduction
2. Nonlinear regression models for individual data
3. Hierarchical linear models
4. Hierarchical nonlinear models
5. Inference based on individual estimates
6. Inference based on linearization
7. Nonparametric and semiparametric inference
8. Bayesian inference
9. Pharmacokinetic and pharmacodynamic analysis
10. Analysis of assay data
11. Further applications
12. Open problems and discussionReadership: Biostatisticians in industry and academia, graduate students accessible to pharmacokineticists and researchers in the clinical and biological sciences
Several books on modelling of repeated measurement data have now appeared, but by and large they describe linear models, with only limited space being devoted to nonlinear models. However, in some types of application, notably in pharmacokinetics, mechanistic nonlinear models are the norm. Since, moreover, such situations naturally predispose them-selves to repeated measurements, the demand for a book such as this one is clear.
The basic statistical model described is that of the hierarchical nonlinear model. This means that the methodology described inherits the computational difficulties of both multilevel models, though the book only deals with one level, and of nonlinear models. Appreciating this is necessary in order to implement and use the methods. The book is restricted to continuous data which leaves obvious scope for yet another book on repeated measurements data!
Chapter 12 describes some open problems, including: the need for stable, well-documented software; research on the validity of the asymptotic approximations used in the theory; the development of diagnostics; issues of measurement error in the covariates; missing data problems; more than one level of nesting; and so on.
The authors aim to keep, and succeed in keeping, the exposition to an intermediate level. Several case studies are described in later chapters.
In summary, this is a valuable addition to the list of books on repeated measures data.
Reviewer: Institute The Open University Place Milton Keynes, U.K. Name D.J. Hand
Title THE JACKKNIFE AND BOOTSTRAP. Author J. Shao and D. Tu. Publisher New York: Springer-Verlag, 1995, pp. xvii + 516, US$49.95. Contents:
1. Introduction
2. Theory of the jackknife
3. Theory of the bootstrap
4. Bootstrap confidence sets and hypothesis tests
5. Computational methods
6. Application to sample surveys
7. Application to linear models
8. Application to nonlinear, nonparametric, and multivariate models
9. Applications to time series and other dependent data
10. Bayesian bootstrap and random weightingReadership: Graduate Students and researchers in statistics interested in resampling methods
The "jackknife" and "bootstrap" are two of the most popular methods among the resampling methods in estimation theory. The basic idea of both methods is to use relatively simple statistics which may be very mediocre in the sense of their statistical efficiency, and then to improve them and to learn something about their properties using resampling. The initial, or seemingly, simplicity of the methods attracted a few practitioners and triggered their popularity. However, quite soon it became evident that the "jackknife" and "bootstrap" produce two other classes of estimators which are not simple to compute and demand rather complicated mathematics to analyze their properties. The present book confirms this fact and its objectives are very similar to what was pursued for other types of estimators. The authors start with some simple examples, then discuss the statistical properties of estimators generated by both approaches. Because the estimators are nonlinear functions of the observations almost all the results have asymptotic character, consistency, asymptotic variance, asymptotic minimaxity, regular and nonregular cases, etc. Then the authors apply the methods to the most popular statistical problems, including model selection, kernel density estimation, discriminant and factor analysis, auto-regression, regression analysis, practically to all problems which are discussed in the standard texts on mathematical statistics. In spite of the fact that both authors are strong disciples of resampling methods, they frequently admit that in most cases the estimators found with the help of traditional approaches work equally well or better.
The book is overloaded with formulae. Probably, this is inevitable, because any concept in re-sampling estimation theory demands twice as much notation as the classical approaches: one has to introduce notations for the basic model, then for its empirical sibling, then for the resampling procedure, then for the secondary ("jackknife" or "bootstrap") estimator and so on.
Undoubtedly, the book is comprehensive and may be a useful reference for many statisticians working within resampling estimation theory.
Reviewer: Institute Oak Ridge National Laboratory Place Oak Ridge, U.S.A. Name V.V. Fedorov
Title LINEAR STATISTICAL MODELS. Author J.H. Stapleton. Publisher New York: Wiley, 1995, pp. xiii + 449, £50.00. Contents:
1. Linear algebra, projections
2. Random vectors
3. The linear model
4. Fitting of regression models
5. Simultaneous confidence limits
6. Two-way and three-way analyses of variance
7. Miscellaneous other models
8. Analysis of frequency dataReadership: Final year undergraduate student and postgraduate student
This is an excellent text, with occasional touches of humour which make it very readable. The table of contents gives little idea of the breadth of topics covered. The first two chapters give a clear and thorough account of the algebraic ideas and distributional theory needed for the rest of the book. This enables the statistical exposition which follows, to proceed in an uncluttered way, with many practical examples. The power of the F-test, examination of residuals, non-linear least squares, robust regression, bootstrap methods, random effects models, split-plot designs and log-linear models are some of the important topics covered. The emphasis is on rigorous theory, but always with practical applications to mind. This is a book which encourages the reader to understand the theoretical concepts behind fitting linear models, which is important in an age when computer packages, useful though they may be in many ways, do not always encourage us to do so.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name L.V. White
Title LINEAR MODELS, LEAST SQUARES AND ALTERNATIVES. Author C.R. Rao and H. Toutenburg. Publisher New York: Springer-Verlag, 1995, pp. xi + 352, US$49.95. Contents:
1. Introduction
2. Linear models
3. The linear regression model
4. The generalized linear regression model
5. Exact and stochastic linear restrictions
6. Prediction problems in the generalized regression model
7. Sensitivity analysis
8. Analysis of incomplete data sets
9. Robust regression
10. Models for binary response variablesReadership: Statistics graduate students, as a text, other disciplines as a reference
After a two-page introductory chapter, the book takes on a surprising aspect by an immediate discussion of regression models in econometrics! It then turns to a general mathematical discussion of ordinary least squares before introducing a set of data with four-factor evaluated via SPSS, which includes a discussion of the stepwise procedure.
As the contents indicate, the book is very wide-ranging and nonstandard, providing details of several subtopics not discussed in such mathematical detail in many other books, and moving on to incomplete data and generalized linear models. Much of the text is mathematically-oriented rather than data-oriented. There are no exercises, but a few examples with data are interspersed. Of its type, the book is idiosyncratic and excellent.
Reviewer: Institute University of Wisconsin Place Madison, U.S.A. Name N.R. Draper
Title PROBABILISTIC RELIABILITY ENGINEERING. Author B.V. Gnedenko and I.A. Ushakov. Publisher New York: Wiley, 1995, pp. xix + 518, £54.00. Contents:
1. Fundamentals
2. Reliability indexes
3. Unrepairable systems
4. Load-strength reliability models
5. Distributions with monotone intensity functions
6. Repairable systems
7. Repairable duplicated systems
8. Analysis of performance effectiveness
9. Two pole networks
10. Optimal redundancy
11. Optimal diagnosis
12. Additional optimization problems in reliability theory
13. Heuristic methods in reliabilityReadership: Engineers involved in reliability assessment, applied probabilists
This book is written by two distinguished Russian scientists, one an engineer and the other an applied mathematician. It gives a distinctly Russian view of the literature and covers various approaches to reliability theory that have evolved over the last two or three decades. The subject of reliability is an increasingly important one as systems become more complex and as the consequences of isolated failures become more critical. The book gives the full background mathematics needed to set up models of reliability and to analyze and design reliable systems using various optimization criteria.
Reviewer: Institute University of Newcastle Place Newcastle, Australia Name G.C. Goodwin
Title THE MALLIAVIN CALCULUS AND RELATED TOPICS. Author D. Nualart. Publisher New York: Springer-Verlag, 1995, pp. xi + 266, US$39.00. Contents:
1. Introduction
2. Analysis on Wiener space
3. Smoothing of probability laws
4. Anticipating stochastic calculus
5. Transformations of the Wiener measureReadership: Researchers in probability and stochastic processes
In the first chapter the differential calculus in the Wiener space is developed. Chapter 2 deals with the regularity of probability laws, existence and smoothness of a density, by means of Malliavin calculus. Among other results there is given a probabilistic proof of the famous Hörmander's "sum of squares" theorem, which was the original motivation for Malliavin calculus. The last two chapters are devoted to other applications of Malliavin calculus: stochastic calculus for anticipating processes and different extensions of the Girsanov theorem for nonlinear and anticipating transforms of the Wiener measure.
Reviewer: Institute Vilnius University Place Vilnius, Lithuania Name V. Paulauskas
Title INTRODUCTION TO STOCHASTIC CALCULUS. Author G.F. Lawler. Publisher New York: Chapman and Hall, 1995, pp. vii + 176, £27.00. Contents:
0. Preliminaries
1. Finite Markov chains
2. Countable Markov chains
3. Continuous-time Markov chains
4. Optimal stopping
5. Martingales
6. Renewal processes
7. Reversible Markov chains
8. Brownian motion
9. Stochastic integrationReadership: Students of theory of applied stochastic processes
Prerequisites for this text include some basic calculus, probability and linear algebra; also for some illustrations and exercises it is assumed that students have access to software for linear algebra computations and writing simple programs. A preliminary chapter contains an introduction to some basic theory of differential and difference equations. Since the readership is intended to include students from a wide variety of disciplines, the treatment does not rely on measure theory, and some of the more mathematical details are omitted. Rather the author seeks to present a careful discussion and motivation of the theory of stochastic processes; the examples in the text and the exercises tend to be mainly restricted to the more basic in preference to drawing in more specialized applications, though, perhaps inevitably, this seems a little limiting in places. However, the approach enables a good number of topics to receive careful treatment in a compact volume.
Reviewer: Institute Imperial College of Science, Technology and Medicine Place London, U.K. Name C.J. Riddler-Rowe
Title STOCHASTIC LIMIT THEORY. An Introduction for Econometricians. Author J. Davidson. Publisher Oxford University Press, 1994, pp. xxii + 539, Can$67.50. Contents:
1. Sets and numbers
2. Limits and continuity
3. Measure
4. Integration
5. Metric spaces
6. Topology
7. Probability spaces
8. Random variables
9. Expectations
10. Conditioning
11. Characteristic functions
12. Stochastic processes
13. Dependence
14. Mixing
15. Martingales
16. Mixingales
17. Near-epoch dependence
18. Stochastic convergence
19. Convergence in Lp-Norm
20. The strong law of large numbers
21. Uniform stochastic convergence
22. Weak convergence of distributions
23. The classical central limit theorem
24. CLTs for dependent processes
25. Some extensions
26. Weak convergence in metric spaces
27. Weak convergence in a function space
28. Cadlag functions
29. FCLTs for dependent variables
30. Weak convergence to stochastic integralsReadership: Mathematical economists, statisticians
The book is intended as an introduction to econometricians of the sophisticated mathematics required to understand the current research in non-stationary random processes. The author provides a rigorous introduction to real analysis, metric spaces, measure theory, and using these tools he introduces stochastic processes from the immediate measure theoretic point of view. In later chapters the emphasis is on the central limit theorem, based on martingale differences. For a reader who is not already familiar with the existing literature on time series and stochastic processes, I feel this book will not be of use. To appreciate the book, one must be very familiar with advanced mathematics, probability theory and time series analysis and it would help if the reader is familiar with J.L. Doob's book on stochastic processes. In this way, I think this book will be a good reference book, rather than an introduction. I wonder how many economists would be interested in functional central limit theorems!
Reviewer: Institute University of Manchester, Institute of Science and Technology Place Manchester, U.K. Name T. Subba Rao
Title ANALYSIS OF ECONOMIC TIME SERIES. A SYNTHESIS, Revised edition. Author M. Nerlove, D.M. Grether and J.L. Carvalho. Publisher San Diego: Academic Press, 1995, pp. xvi + 468, US$34.95. Contents:
1. A history of the idea of unobserved components in the analysis of economic time series
2. Introduction to the theory of stationary time series
3. The spectral representation and its estimation
4. Formulation and analysis of unobserved-components models
5. Elements of the theory of prediction and extraction
6. Formulation of unobserved-components models and canonical forms
7. Estimation of unobserved-components and canonical models
8. Appraisal of seasonal adjustment techniques
9. On the comparative structure of serial dependence in some U.S. price series
10. Formulation and estimation of multivariate mixed moving-average autoregressive models for single time-series: Examples
11. Formulation and estimation of multivariate mixed moving-average autoregressive time-series models
12. Formulation and estimation of unobserved-components models: Examples
13. A time-series model of the U.S. cattle industry
APPENDIX A: The Work of Buys Ballot
APPENDIX B: Some Requisite Theory of Functions of a Complex Variable
APPENDIX C: Fourier Series and Analysis
APPENDIX D: Whittle's Theorem
APPENDIX E: Inversion of Tridiagonal Matrices and a Method for Inverting Toeplitz Matrices
APPENDIX F: Spectral Densities, Actual and Theoretical, Eight Series
APPENDIX G: Derivation of a Distributed-Lag Relation between Sales and Production: A Simple ExchangeReadership: Econometricians, statisticians
Time series models such as autoregressive integrated moving average (ARIMA) models (Box and Jenkins Model) and distributed lag models are often used in recent years to describe many economic time series. The interesting aspect of this book is that the authors have provided both frequency domain and time domain approaches to the estimation of the parameters of the models. The unique feature in this book is Wiener's approach to filtering using the notion introduced by P. Whittle in his classic little monograph. I have not seen any book so far in economics which has considered this approach, nor for that matter the frequency domain approach. It is an extremely well-written book though very hard for a researcher who is not familiar with these approaches and I recommend every economist to read it.
Reviewer: Institute University of Manchester, Institute of Science and Technology Place Manchester, U.K. Name T. Subba Rao
Title TOPICS IN THE CONSTRUCTIVE THEORY OF COUNTABLE MARKOV CHAINS. Author G. Fayolle, V.A. Malyshev and M.V. Menshikov. Publisher Cambridge University Press, 1995, pp. 169, £27.95/ US$44.95. Contents:
Introduction and history
1. Preliminaries
2. General criteria
3. Explicit construction of Lyapounov functions
4. Ideology of induced chains
5. Random walks in two-dimensional complexes
6. Stability
7. Exponential convergence and analyticityReadership: Probabilists and engineers working with Markov chains
This book provides methods allowing a complete classification of Markov chains as ergodic, null-recurrent or transient. Moreover, the constructive use of the method of Lyapounov functions permits the authors to study stability with respect to parameters.
Chapter 1 is introductory and contains basic definitions and results from continuous Markov chains. In Chapter 2 the main classification criteria for general countable Markov chains are presented. The rest of the book is devoted to the so-called deflected random walks in ZN which provide a useful scheme for considering general networks. In Chapter 3 techniques for an explicit geometrical construction of Lyapounov functions are considered. In Chapter 4 the method of induced chains and vector fields are presented, and a complete classification of the Markov chains in R3 is obtained. A new feature called scattering is considered in Chapter 5. Continuity and stability with respect to parameters are considered in Chapter 6. Chapter 7 contains a probabilistic criterion for a family of Markov chains to be an analytic Lyapunov family. The last property leads to the analytic dependence on parameters, exponential convergence to equilibrium and exponential decrease of stationary probability.
The authors are experts in the subject and the monograph is based mainly on their earlier results.
Reviewer: Institute Macquarie University Place Sydney, Australia Name A.S. Kozek
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