Asymptotic Theory of Testing Statistical Hypotheses

, by Bening, Vladimir E.

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ISBN: 9789067643238 | 9067643238
Cover: Hardcover
Copyright: 6/1/2000

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Supplemental Materials

Foreword

iii

Preface

vii

Notations

xix

Asymptotic test theory

(48)

First-order asymptotic theory

(6)

Second order efficiency

(3)

On efficiency of first and second order

(3)

Power loss

(2)

Efficiency and deficiency

(26)

Deficiency results for the symmetry problem

(8)

Asymptotic expansions under alternatives

(22)

Introduction

(3)

A formal rule

(4)

General Theorem

(2)

Proof of General Theorem

(4)

L-, R-, and U-statistics

(3)

Auxiliary lemmas

(6)

Power loss

(54)

Introduction

(3)

General theorem

(6)

Tests based on L-, R-, and U-statistics

(7)

Proof of General Theorem: Lemmas

(1)

Proof of Lemmas

(10)

Power loss for L-, R-, and U-tests

(8)

Proofs of Theorems

106

(4)

Combined L-tests

110

(7)

Other statistics

117

(8)

Edgeworth expansion for the likelihood ratio

125

(24)

Introduction

125

(9)

Moment conditions

134

(7)

Case of independent but not identically distributed terms

141

(8)

A LeCam's Third Lemma

149

(8)

B Convergence rate under alternatives

157

(22)

B.1 General theorem

157

(3)

B.2 Proof of Theorem B.1.1

160

(4)

B.3 L-,R-, and U-statistics

164

(3)

B.4 Proof of Theorem B.3.1

167

(12)

C Proof of Theorem 1.3.1

179

(4)

D The Neyman-Pearson Lemma

183

(2)

E Edgeworth expansions

185

(16)

F Proof of Lemmas 2.6.1-2.6.5

201

(14)

F.1 Proof of Lemma 2.6.1

201

(1)

F.2 Proof of Lemma 2.6.2

202

(2)

F.3 Proof of Lemma 2.6.3

204

(4)

F.4 Proof of Lemma 2.6.4

208

(5)

F.5 Proof of Lemma 2.6.5

213

(2)

G Proof of Lemma 3.7.1-3.7.5

215

(14)

G.1 Proof of Lemma 3.7.1

215

(1)

G.2 Proof of Lemma 3.7.2

216

(3)

G.3 Proof of Lemma 3.7.3

219

(3)

G.4 Proof of Lemma 3.7.4

222

(1)

G.5 Proof of Lemma 3.7.5

223

(6)

H Asymptotically complete classes

229

(10)

H.1 Non-asymptotic theorem on complete classes

229

(2)

H.2 Asymptotic theorem on complete classes

231

(4)

H.3 Power functions of complete classes

235

(4)

I Higher order asymptotics for R-,L-, and U-statistics

239

(16)

I.1 R-statistics

239

(7)

I.2 L-statistics

246

(5)

I.3 U-statistics

251

(2)

I.4 Symmetric statistics

253

(2)

Bibliography

255

(16)

Subject Index

271

(4)

Author Index

275

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Asymptotic Theory of Testing Statistical Hypotheses

Table of Contents

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