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CONTENTS
CHAPTER
1 THE GENERAL DECISION PROBLEM ... 1
1 Statistical inference and statistical decisions ... 1
2 Specification of a decision problem ... 2
3 Randomization ; choice of experimen...
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목차 전체
CONTENTS
CHAPTER
1 THE GENERAL DECISION PROBLEM ... 1
1 Statistical inference and statistical decisions ... 1
2 Specification of a decision problem ... 2
3 Randomization ; choice of experiment ... 6
4 Optimum procedures ... 8
5 Invariance and umbiasedness ... 10
6 Bayes and minimax procedures ... 14
7 Maximum likelihood ... 16
8 Complete classes ... 17
9 Sufficient statistics ... 18
10 Problems ... 22
11 References ... 28
2 THE PROBABILITY BACKGROUND ... 34
1. Probability and measure ... 34
2 Integration ... 37
3 Statistics and subfield ... 41
4 Conditional expectation and probability ... 43
5 Conditional probability distributions ... 48
6 Characterization of sufficiency ... 53
7 Exponential families ... 57
8 Problems ... 60
9 References ... 66
3 UNIFORMLY MOST POWERFUL TESTS ... 68
1 Stating the problem ... 68
2 The Neyman-Person fundamental lemma ... 72
3 Distributions with monotone likelihood ratio ... 78
4 Comparison of experiments ... 86
5 Confidence bounds ... 89
6 A generalization of the fundamental lemma ... 96
7 Two-sided hypotheses ... 101
8 Least favorable distributions ... 104
9 Testing the mean and variance of a normal distribution ... 108
10 Problems ... 111
11 References ... 126
4 UNBIASEDNESS : THEORY AND FIRST APPLICATIONS ... 134
1 Unbiasedness for hypothesis testing ... 134
2 One-parameter exponential families ... 135
3 Similarity and completeness ... 140
4 UMP unbiased tests for multiparameter exponential families ... 145
5 Comparing two Poisson or binomial populations ... 151
6 Testing for independence in an 2 × 2 table ... 156
7 Alternative models for 2 × 2 table ... 159
8 Some three-factor contingency tables ... 162
9 The sign test ... 166
10 Problems ... 170
11 References ... 181
5 UNBIASEDNES : APPLICATIONS TO NORMAL DISTRIBUTIONS ; CONFIDENCE INTERBALS ... 188
1 Statistics independent of a sufficient statistic ... 188
2 Testing the parameters of a normal distribution ... 192
3 Comparing the means and bariances of tow normal distributions ... 197
4 Robustness ... 203
5 Effect of dependence ... 209
6 Confidence interval and families of tests ... 213
7 Unbiased confidences sets ... 216
8 Regression ... 222
9 Bayesian confidences sets ... 225
10 Permutation tests ... 230
11 Most powerful permutation tests ... 232
12 Randomization as a basis for inference ... 237
13 Permutation tests and randomization ... 240
14 Randomization model and confidences intervals ... 245
15 Testing for independence in a bivariate normal distribution ... 248
16 Problems ... 253
17 References ... 273
6 INVARIANCE ... 282
1 Symmetry and invariance ... 282
2 Maximal invariants ... 284
3 Most powerful invariant tests ... 289
4 Sample inspection by variables ... 293
5 Almost invariance ... 297
6 Unbiasedness and invariance ... 302
7 Admissibility ... 305
8 Rank tests ... 314
9 The two-sample problem ... 317
10 The hypothesis of symmetry ... 323
11 Equivariant confidence sets ... 326
12 Average smallest equibariant confidence sets ... 330
13 Confidence bands for a distribution function ... 334
14 Problems ... 337
15 References ... 357
7 LINEAR HYPOTHESES ... 365
1 A canonical form ... 365
2 Linear hypotheses and least squares ... 370
3 Tests of homogeneity ... 374
4 Multiple comparisons ... 380
5 Two-way layout : One observation per cell ... 388
6 Two-way layout : m observation per cell ... 392
7 Regression ... 396
8 Robustness against nonnormality ... 401
9 Scheff e ´ s S-method : A special case ... 405
10 Scheff e ´ s S-method for general linear models ... 411
11 Random-effects model : One-way classification ... 418
12 Nested classifications ... 422
13 problems ... 427
14 References ... 444
8 MULTIVARIATE LINEAR HYPOTHESES ... 453
1 A canonical form ... 453
2 Reduction by invariance ... 456
3 The one-and two-sample problems ... 459
4 Multivariate analysis of variance (MANOVA) ... 462
5 Further applications ... 465
6 Simultaneous confidence intervals ... 471
7 χ2 -tests : Simple hypothesis and unrestricted alternatives ... 477
8 χ2 -and likelihood-ratio tests ... 480
9 Problems ... 488
10 References ... 498
9 THE MINIMAX PRINCIPLE ... 504
1 Tests with guaranteed power ... 504
2 Examples ... 508
3 Comparing two approximate hypotheses ... 512
4 Maximin tests and invariance ... 516
5 The Hunt-Stein theorem ... 519
6 Most stringent tests ... 525
7 Problems ... 527
8 References ... 535
10 CONDITIONAL INFERENCE ... 539
1 Mixtures of experiments ... 539
2 Ancillary statistics ... 542
3 Optimal conditional tests ... 549
4 Relevant subsets ... 553
5 Problems ... 559
6 References ... 564
APPENDIX ... 569
1 Equivalence relations ; groups ... 569
2 Convergence of distributions ... 570
3 Dominated families of distributions ... 574
4 The weak compactness theorem ... 576
5 References ... 577
AUTHOR INDEX ... 579
SUBJECT INDEX ... 587
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