Lieshout, M.N.M. (Marie-Colette) van

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case, in finite samples, the essentially unique optilllU!ll unbiased estimating equation. The treatme-nt using asymptotics tends to suggest to students that maximum like! H:hood estimation is superior to other methods only in large samples. University of Essex Colchester, U.K. G.A. Barnard PlAIN ANSWERS TO COMPLEX QU~ST!ONS, 2nd edition. R. Christensen. New York: Springer·Verlag, 1996, pp. xvii + 452, US$54.95. Contents: 1. Introduction 2. Estimation 3. Testing hypotheses 4. One-way ANOVA 5. Multiple c~arison techniques 6. Regression analysis 7. Mu!tifactor analysis of variance 8. Experimental design 9. Analysis of covariance 10. Estimation and testing in general Gauss-Markov models 11. Split plot models 12. Mixed models and variance components 13. Checking assumptions, residuals, and influential observations 14. Variable selection and co\ linearity Readership: Mathematically prepared readers This revision of the original 1987 book [Short Book Reviews, Vol. 8, p.3] retains its fairly mathe-matical character and has gone from 380 to 452 pages, a nineteen percent increase. log· linear models, the former Chapter 15, and the former "Appendix F: Approxi· mate methods for unbalanced ANOVAs" are gone, and there is more on "ANO\IA·type" models and a new Appendix F. The writing style is inviting and the text often ex· presses the author's feelings in friendly and affable ways. The computing aspects of regression are de· emphasized and the text leans more towards well· prepared statistics students. If you t iked the first edition, I did, you will be pleased by the second. There are one hundred and twenty-six references. University of Wisconsin Madison, U.S.A. 11.R. Draper THE STATISTICAL THEORY OF SHAPE. C.G. Small. New York: Springer-Ver!ag, 1996, pp. x + 227, US$ 49.95. Contents: 1. Introduction 2. Background concepts and definitions 3. Shape spaces 4. Some stochastic geometry 5. Distributions of random shapes 6. Some examples of shape analysis Readership: Statisticians, probabilists and experimental scientists with some background in differential geometry The •shape' of an object is what remains after all information regarding size, location and orien· tation is discarded. For example, all squares share the same shape. In the early 1980s, a formal theory of shape was developed, albeit from different perspec-tives, by D.G. Kendall and F. Bookstein. More recen-tly, the subject has found applications in areas as diverse as archaeology, biology, medicine and vision. Although some excellent reviews exist, a textbook solely devoted to shape analysis seems to be missing. 4 The present monograph will be a useful introduction for anyone interested in shape, as well as a helpful source of reference fer researchers in the field. University of Warwick Coventry, U.K. M.C. van Lieshout STATISTICAL METHODS: A GEOMETRIC PRIMER. D.J. Saville and G.R. l./ood. New York: Springer·Verlag, 1996, pp. xi + 268, US$39.95. Contents: 1. Introduction 2. Paired samples 3. Independent samples 4. Several independent samples 5. Simple regression 6. Overview APPENDIX A: Geometric Tool Kit APPENDIX B: Statistical Tool Kit APPENDIX C: Computing APPENDIX D: Alternative Test Statistic APPENDIX E: Solutions to Exercises Readership: Undergraduate statistics students and teachers At the heart of the linear model is the Pythagorean triangle, which decomposes the data into a component corresponding to a fitted regression and a component corresponding to error. Despite the sim-pl iclty of this idea, we all know that students have a hard time understanding the geometric interpretation of basic linear methods. However, the combined tools of projection and orthogonal decomposition are essen· tiat ingredients in an undergraduate understanding of statistics. Much of our discipline is concerned with the extraction of signal from noise, where projection is the tool for the job. However, the task of ex· plaining the geometry of the linear model is not easy. Realistic sets of data live in high dimensions that cannot be graphed on a page. Nevertheless, the authors of this book have done an excellent job of explaining clearly what needs to be said. I would particularly recorrrnend it as a supplementary text in an under· graduate course. Among the mass-market statistics cook· books, it makes a refreshing change. University of Waterloo l./aterloo, Canada C.G. Small UNBIASEO ESTIMATORS AND THEIR APPLICATIONS. VOLUME 2: MULTIVARIATE CASE. V.G. Vionov and M.S. Nikulin. Dordrecht: Kluwer, 1996, pp. ix + 262, Of!.195.00/US$135.00/£88.00. Contents: 1. Basic remarks on multivariate probability distributions 2. Elements of the theory of point statistical estimation in the multivariate case 3. Techniques for constructing unbiased estimators 4. Applications of unbiased estimators APPENDIX 1: Tables of Unbiased Estimators APPENDIX 2: On Evaluating Some Multivariate Integrals APPENDIX 3: Partitions and Some Multivariate Statistical Problems Readership: Researchers in multivariate theory Those working on estimation problems involving multivariate distributions will find this book a useful addition to their library. It follows on from Unbiased Estimators and Ihtlr. Applications.~ 1: Univariate 

The statistical theory of shape

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