Theoretical StatisticsA text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistical procedures. Chapters 4 and 5 cover hypothesis testing with simple and null hypotheses, respectively. Subsequent chapters discuss non-parametrics, interval estimation, point estimation, asymptotics, Bayesian procedure, and deviation theory. Student familiarity with standard statistical techniques is assumed. |
Contents
Bibliographic notes | 10 |
11 | 37 |
Bibliographic notes | 56 |
Chapter 3 | 65 |
Bibliographic notes | 125 |
composite null hypotheses | 131 |
Bibliographic notes | 174 |
Bibliographic notes | 202 |
Bibliographic notes | 406 |
Chapter 4 | 424 |
Bibliographic notes | 474 |
Author Index | 496 |
simple null hypotheses | |
Decision theory 412 | |
Further results and exercises 459 | 459 |
Order statistics 466 | 466 |
Bibliographic notes | 246 |
Bibliographic notes | 272 |
Further results and exercises | 356 |
Bayesian methods | 364 |
Bibliographic notes 474 | 474 |
| 496 | |
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Common terms and phrases
alternative analysis ancillary statistic apply approximation arbitrary argument asymptotically normal Bayes Bayes's theorem Bayesian bution calculation Chapter chi-squared distribution conditional distribution confidence intervals confidence limits confidence region consider corresponding critical region decision rule defined degrees of freedom derived discussion distri equation equivalent Example exponential family fy(y given independent J.R. Statist Let Y₁ likelihood function likelihood principle likelihood ratio linear model m.l. ratio matrix maximal invariant methods minimal sufficient statistic n₁ normal distribution normal-theory nuisance parameters null hypothesis observations obtained order statistics parameter space parameter values particular permutation Poisson distribution possible posterior distribution principle prior density prior distribution probability problem procedure properties random variables regression risk function sample Section significance test similar regions simple situation sufficient statistic Suppose that Y₁ test statistic theory transformations unbiased estimate uniformly most powerful unknown parameters vector Y₂ Yn be i.i.d. zero