Testing Statistical Hypotheses
By: by E. L. Lehmann
Edition: Second Edition.
Series: Springer Texts in Statistics; Springer Texts in Statistics
Publisher: Springer New York; Springer
Published: 1986
Place of publication: New York, NY
Language: eng
Number of pages: 604
ISBN-13: 9781475719239; 9781475719253
Subjects: Statistics; Mathematical statistics; Statistical Theory and Methods; Statistics for Life Sciences, Medicine, Health Sciences
Description: This new edition reflects the development of the field of hypothesis testing since the original book was published 27 years ago, but the basic structure has been retained. In particular, optimality considerations con­ tinue to provide the organizing principle. However, they are now tempered by a much stronger emphasis on the robustness properties of the resulting procedures. Other topics that receive greater attention than in the first edition are confidence intervals (which for technical reasons fit better here than in the companion volume on estimation, TPE*), simultaneous in­ ference procedures (which have become an important part of statistical methodology), and admissibility. A major criticism that has been leveled against the theory presented here relates to the choice of the reference set with respect to which performance is to be evaluated. A new chapter on conditional inference at the end of the book discusses some of the issues raised by this concern. In order to accommodate the wealth of new results that have become available concerning the core material, it was necessary to impose some limitations. The most important omission is an adequate treatment of asymptotic optimality paralleling that given for estimation in TPE. Since the corresponding theory for testing is less satisfactory and would have required too much space, the earlier rather perfunctory treatment has been retained. Three sections of the first edition were devoted to sequential analysis.
Table of contents: title: 1 The General Decision Problem; title: 2 The Probability Background; title: 3 Uniformly Most Powerful Tests; title: 4 Unbiasedness: Theory and First Applications; title: 5 Unbiasedness: Applications to Normal Distributions; Confidence Intervals; title: 6 Invariance; title: 7 Linear Hypotheses; title: 8 Multivariate Linear Hypotheses; title: 9 The Minimax Principle; title: 10 Conditional Inference; title: 1 Equivalence relations; groups; title: 2 Convergence of distributions; title: 3 Dominated families of distributions; title: 4 The weak compactness theorem; title: 5 References; title: Author Index.