Asymptotic theory of testing statistical hypotheses: efficient statistics, optimality, power loss and deficiency
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht [u.a.]
VSP
2000
|
| Edition: | 1. publ. |
| Series: | Modern probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 277 S. |
| ISBN: | 9067643238 9067643017 |
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Record in the Search Index
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| adam_text | Titel: Asymptotic theory of testing statistical hypotheses
Autor: Bening, Vladimir E.
Jahr: 2000
Contents
Foreword iii
Preface vii
Notations xix
1 Asymptotic test theory 1
1.1 First-order asymptotic theory........................ 1
1.2 Second order efficiency............................ 7
1.3 On efficiency of first and second order.................... 10
1.4 Power loss ................................... 13
1.5 Efficiency and deficiency........................... 15
1.6 Deficiency results for the symmetry problem................ 41
2 Asymptotic expansions under alternatives 49
2.1 Introduction.................................. 49
2.2 A formal rule.................................. 52
2.3 General Theorem............................... 56
2.4 Proof of General Theorem........................... 58
2.5 L-, R-, and U -statistics............................ 62
2.6 Auxiliary lemmas............................... 65
3 Power loss 71
3.1 Introduction.................................. 71
3.2 General theorem................................ 74
3.3 Tests based on L-, R-, and U-statistics................... 80
3.4 Proof of General Theorem: Lemmas..................... 87
3.5 Proof of Lemmas................................ 88
3.6 Power loss for L-,R-, and U-tests...................... 98
3.7 Proofs of Theorems .............................. 106
3.8 Combined L-tests............................... 110
3.9 Other statistics................................. 117
4 Edgeworth expansion for the likelihood ratio 125
4.1- Introduction.................................. 125
4.2 Moment conditions .............................. 134
4.3 Case ofindependent but not identically distributed terms........ 141
A LeCam s Third Lemma 149
B Convergence rate under alternatives 157
B.I General theorem................................ 157
B.2 Proof of Theorem B.I.I............................ 160
B.3 L-, R-, and U-statistics............................ 164
B.4 Proof of Theorem B.3.1............................ 167
C Proof of Theorem 1.3.1 179
D The Neyman-Pearson Lemma 183
E Edgeworth expansions 185
F Proof of Lemmas 2.6.1-2.6.5 201
F.I Proof of Lemma 2.6.1............................. 201
F.2 Proof of Lemma 2.6.2............................. 202
F.3 Proof of Lemma 2.6.3............................. 204
F.4 Proof of Lemma 2.6.4............................. 208
F.5 Proof of Lemma 2.6.5............................. 213
G Proof of Lemmas 3.7.1-3.7.5 215
G.I Proof of Lemma 3.7.1............................. 215
G.2 Proof of Lemma 3.7.2............................. 216
G.3 Proof of Lemma 3.7.3............................. 219
G.4 Proof of Lemma 3.7.4............................. 222
G.5 Proof of Lemma 3.7.5............................. 223
H Asymptotically complete classes 229
H.I Non-asymptotic theorem on complete classes ............... 229
H.2 Asymptotic theorem on complete classes.................. 231
H.3 Power functions of complete classes..................... 235
I Higher order asymptotics for R-, L-, and U-statistics 239
1.1 R-statistics................................... 239
1.2 L-statistics................................... 246
1.3 U-statistics................................... 251
1.4 Symmetric statistics.............................. 253
Bibliography 255
Subject Index 271
Author Index 275
|
| any_adam_object | 1 |
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| dewey-search | 519.5/6 |
| dewey-sort | 3519.5 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV013451865 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:10Z |
| institution | BVB |
| isbn | 9067643238 9067643017 |
| language | English |
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| physical | XXII, 277 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | VSP |
| record_format | marc |
| series2 | Modern probability and statistics |
| spelling | Bening, Vladimir E. Verfasser aut Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency Vladimir E. Bening 1. publ. Utrecht [u.a.] VSP 2000 XXII, 277 S. txt rdacontent n rdamedia nc rdacarrier Modern probability and statistics Teoria assintótica (inferência estatística) larpcal Testes de hipóteses larpcal Asymptotic expansions Statistical hypothesis testing HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009182809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bening, Vladimir E. Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency Teoria assintótica (inferência estatística) larpcal Testes de hipóteses larpcal Asymptotic expansions Statistical hypothesis testing |
| title | Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency |
| title_auth | Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency |
| title_exact_search | Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency |
| title_full | Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency Vladimir E. Bening |
| title_fullStr | Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency Vladimir E. Bening |
| title_full_unstemmed | Asymptotic theory of testing statistical hypotheses efficient statistics, optimality, power loss and deficiency Vladimir E. Bening |
| title_short | Asymptotic theory of testing statistical hypotheses |
| title_sort | asymptotic theory of testing statistical hypotheses efficient statistics optimality power loss and deficiency |
| title_sub | efficient statistics, optimality, power loss and deficiency |
| topic | Teoria assintótica (inferência estatística) larpcal Testes de hipóteses larpcal Asymptotic expansions Statistical hypothesis testing |
| topic_facet | Teoria assintótica (inferência estatística) Testes de hipóteses Asymptotic expansions Statistical hypothesis testing |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009182809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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