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**Testing statistical hypotheses.
3rd ed.**
*(English)*
Zbl 1076.62018

Springer Texts in Statistics. New York, NY: Springer (ISBN 0-387-98864-5/hbk). xiv, 784 p. (2005).

This is a revised and expanded version of the well-known second edition from 1986; see the review Zbl 0608.62020. The present volume is divided into two parts. Part I (chapters 1–10) treats small-sample theory, while Part II (chapters 11–15) treats large-sample theory.

The fist part covers more or less the related body of the text of the second edition. Some material found there, especially the chapter on multivariate linear hypotheses, has been eliminated in order to make room for additions as most of Part II and the new chapter 9 on a comprehensive treatment of multiple testing including some recent optimality results.

Various large-sample considerations that in the second edition were discussed in earlier chapters now have been moved to Part II ‘Large-Sample Theory’, especially to chapter 11. Chapters 11 and 12 present the large-sample tools needed for treating asymptotic optimality in chapter 13. These tools are are also used in chapter 14 to give a much fuller treatment of tests of goodness of fit than was given in the 2nd edition, and in chapter 15 an introduction to bootstrap and related techniques is provided. Every chapter is supplemented with a rich collection of problems and notes about historic development and hints to the literature.

The third edition of ‘Testing Statistical Hypotheses’ brings it into consonance with the second edition of its companion volume on point estimation [E. L. Lehmann and G. Casella, Theory of point estimation. 2nd ed. (1998; Zbl 0916.62017)]. The exposition is clear and sufficiently rigorous. As was stated in the review of the second edition, much of the first part of the book can be read without knowledge of measure theory although familiarity with it will be of much help. But the second part is more demanding.

With this edition, ‘Testing Statistical Hypotheses’ will undoubtedly continue to be the standard graduate level textbook on statistical testing.

The fist part covers more or less the related body of the text of the second edition. Some material found there, especially the chapter on multivariate linear hypotheses, has been eliminated in order to make room for additions as most of Part II and the new chapter 9 on a comprehensive treatment of multiple testing including some recent optimality results.

Various large-sample considerations that in the second edition were discussed in earlier chapters now have been moved to Part II ‘Large-Sample Theory’, especially to chapter 11. Chapters 11 and 12 present the large-sample tools needed for treating asymptotic optimality in chapter 13. These tools are are also used in chapter 14 to give a much fuller treatment of tests of goodness of fit than was given in the 2nd edition, and in chapter 15 an introduction to bootstrap and related techniques is provided. Every chapter is supplemented with a rich collection of problems and notes about historic development and hints to the literature.

The third edition of ‘Testing Statistical Hypotheses’ brings it into consonance with the second edition of its companion volume on point estimation [E. L. Lehmann and G. Casella, Theory of point estimation. 2nd ed. (1998; Zbl 0916.62017)]. The exposition is clear and sufficiently rigorous. As was stated in the review of the second edition, much of the first part of the book can be read without knowledge of measure theory although familiarity with it will be of much help. But the second part is more demanding.

With this edition, ‘Testing Statistical Hypotheses’ will undoubtedly continue to be the standard graduate level textbook on statistical testing.

Reviewer: Rainer Schlittgen (Hamburg)