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Tables of Contents for Theoretical Statistics
Chapter/Section Title
Page #
Page Count
Preface
xi
Introduction
1
10
Objectives of statistical analysis and theory
1
4
Criteria for the choice of families of models
5
2
The analysis of complex responses
7
1
Plan of the book
8
3
Bibliographic notes
10
1
Some general concepts
11
53
The likelihood
11
7
Sufficient statistics
18
18
Some general principles of statistical inference
36
9
Some approaches to statistical inference
45
19
Bibliographic notes
56
2
Further results and exercises
58
6
Pure significance tests
64
24
Null hypotheses
64
2
Test statistics and their null distributions
66
7
Composite null hypotheses
73
3
Discussion
76
12
Bibliographic notes
82
1
Further results and exercises
83
5
Significance tests: simple null hypotheses
88
43
General
88
2
Formulation
90
1
Simple null hypothesis and simple alternative hypothesis
91
2
Some examples
93
6
Discrete problems
99
2
Composite alternatives
101
4
Two-sided tests
105
1
Local power
106
15
Multidimensional alternatives
121
10
Bibliographic notes
125
1
Further results and exercises
126
5
Significance tests: composite null hypotheses
131
48
General
131
3
Similar regions
134
23
Invariant tests
157
14
Some more difficult problems
171
8
Bibliographic notes
174
1
Further results and exercises
175
4
Distribution-free and randomization tests
179
28
General
179
3
Permutation tests
182
5
Rank tests
187
9
Randomization tests
196
2
Distance tests
198
9
Bibliographic notes
202
1
Further results and exercises
203
4
Interval estimation
207
43
Introduction
207
1
Scalar parameter
208
20
Scalar parameter with nuisance parameters
228
8
Vector parameter
236
6
Estimation of future observations
242
8
Bibliographic notes
246
1
Further results and exercises
247
3
Point estimation
250
29
General
250
2
General considerations on bias and variance
252
2
Cramer-Rao inequality
254
4
Achievement of minimum variance and removal of bias
258
8
Estimates of minimum mean squared error
266
4
Robust estimation
270
9
Bibliographic notes
272
1
Further results and exercises
273
6
Asymptotic theory
279
85
Introduction
279
4
Maximum likelihood estimates
283
28
Large-sample parametric significance tests
311
33
Robust inference for location parameters
344
20
Bibliographic notes
354
2
Further results and exercises
356
8
Bayesian methods
364
48
Introduction
364
1
Bayes's theorem
365
4
Conjugate prior distributions
369
6
Interpretation of Bayesian probability statements
375
15
Bayesian versions of some previous types of procedure
390
9
Asymptotic Bayesian theory
399
1
Empirical Bayes procedures
400
12
Bibliographic notes
406
1
Further results and exercises
406
6
Decision theory
412
50
Examples of statistical decision problems
412
3
Formulation of terminal decision problems
415
2
Solution of the fully specified terminal decision problem
417
9
Utility
Incompletely specified decision problems
426
3
Decision theory without prior distributions
429
12
Decision theory representation of common problems
441
4
A remarkable case of inadmissibility
445
6
Sequential decision problems
451
11
Bibliographic notes
458
1
Further results and exercises
459
3
Appendix 1 Determination of probability distributions
462
4
Appendix 2 Order statistics
466
9
A2.1 General properties
466
1
A2.2. Special distributions
467
1
A2.3. Asymptotic distributions
468
2
A2.4. Linear combinations of order statistics
470
2
A2.5. Extreme value theory
472
3
Bibliographic notes
474
1
Appendix 3 Second-order regression for arbitrary random variables
475
3
References
478
18
Author Index
496
3
Subject Index
499