Testing Statistical HypothesesThe Third Edition of Testing Statistical Hypotheses brings it into consonance with the Second Edition of its companion volume on point estimation (Lehmann and Casella, 1998) to which we shall refer as TPE2. We won’t here comment on the long history of the book which is recounted in Lehmann (1997) but shall use this Preface to indicate the principal changes from the 2nd Edition. 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 preface to the 2nd Edition stated that “the most important omission is an adequate treatment of optimality paralleling that given for estimation in TPE.” We shall here remedy this failure by treating the di?cult topic of asymptotic optimality (in Chapter 13) together with the large-sample tools needed for this purpose (in Chapters 11 and 12). Having developed these tools, we use them in Chapter 14 to give a much fuller treatment of tests of goodness of ?tthan was possible in the 2nd Edition, and in Chapter 15 to provide an introduction to the bootstrap and related techniques. Various large-sample considerations that in the Second Edition were discussed in earlier chapters now have been moved to Chapter 11. |
Contents
| 3 | |
| 10 | |
| 28 | |
Invariance | 212 |
Problems | 265 |
Linear Hypotheses | 277 |
The Minimax Principle | 319 |
Uniformly Most Powerful Tests | 340 |
Large Sample Optimality | 527 |
8 | 573 |
Testing Goodness of Fit | 583 |
General Large Sample Methods | 631 |
A Auxiliary Results | 692 |
References | 702 |
Distributions with Monotone Likelihood Ratio | 714 |
10 | 725 |
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Common terms and phrases
alternatives Annals of Statistics apply Assume assumptions asymptotic bootstrap Borel sets conditional distribution confidence intervals confidence sets consider convergence covariance matrix cumulative distribution function defined denote determined distribution function equivalent equivariant estimator Example exists a UMP exponential family finite fixed follows given group G hence hypothesis H implies independently distributed Lebesgue measure Lemma Let X1 level-a test linear matrix maximal invariant mean measure normal distribution null hypothesis obtained P₁ parameter permutation power function probability density problem of testing procedure proof random variable real-valued rejection region respect result risk functions sample satisfying Section sequence Slutsky's Theorem space subset sufficient statistic Suppose t-test test of H test statistic testing H Theorem transformations UMP invariant test UMP test UMP unbiased test uniformly most accurate values vector Y₁ zero σ²