Contiguity of Probability Measures: Some Applications in Statistics

Cover......Page 1
Frontmatter......Page 2
Contents......Page 8
Acknowledgement......Page 11
Preface......Page 12
Summary......Page 16
1 Some preliminary definitions and results......Page 17
2 Contiguity and its relation to other concepts of `nearness\' of sequences of probability measures......Page 22
3 Alternative characterizations of contiguity......Page 25
4 Some auxiliary results......Page 33
5 Proof of Proposition 3.1......Page 40
6 An additional characterization of contiguity......Page 46
7 Some results following from contiguity......Page 48
Exercises......Page 54
Summary......Page 56
1 Preliminaries......Page 57
2 Assumptions......Page 60
3 Some examples......Page 62
4 Asymptotic expansion and asymptotic normality of likelihood functions......Page 67
5 Some lemmas......Page 69
6 Proof of theorems of Section 4......Page 78
Exercise......Page 81
Summary......Page 82
1 Formulation of the problem and some preliminary results......Page 83
2 Some auxiliary results......Page 87
3 The proof of the theorem......Page 91
4 Differential equivalence of sequences of probability measures and differential sufficiency......Page 94
5 Some statistical implications of Theorem 1.1......Page 96
Exercises......Page 99
Summary......Page 100
1 Additional assumptions -- Examples......Page 101
2 Some lemmas......Page 111
3 Testing a simple hypothesis against one-sided alternatives......Page 114
4 AUMP tests for the examples of Section 1......Page 120
5 Testing a simple hypothesis against two-sided alternatives......Page 122
6 Testing a one-sided hypothesis against one-sided alternatives......Page 138
Exercises......Page 142
1 W-efficiency -- preliminaries......Page 143
2 Some lemmas......Page 146
3 A representation theorem......Page 150
4 W-efficiency of estimates: upper bounds via Theorem 3.1......Page 156
5 W-efficiency of estimates: upper bounds......Page 162
6 Asymptotic efficiency of estimates: the classical approach......Page 172
7 Classical efficiency of estimates: the multiparameter case......Page 175
Exercise......Page 181
1 Some notation and preliminary results......Page 182
2 Formulation of some of the main results......Page 184
3 Restriction to the class of tests [SCRIPT CAPITAL F]......Page 186
4 Proof of the first main result......Page 192
5 Proof of the second main result......Page 199
6 Formulation and proof of the third main result......Page 203
7 Behaviour of the power under non-local alternatives......Page 211
Exercises......Page 212
1 Some theorems employed in Chapter 1......Page 214
2 Some theorems employed in Chapter 2......Page 219
Exercise......Page 238
3 A theorem employed in Chapter 5......Page 239
4 Some theorems employed in Chapter 6......Page 240
Exercises......Page 254
Bibliography......Page 255
Index......Page 261