Sequential methods in statistics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Chapman and Hall
1986
|
| Edition: | 3. ed. |
| Series: | Monographs on statistics and applied probability
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 264 S. |
| ISBN: | 0412281503 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface Page ix
1 Introduction 1
1.1 Sequential experiments 1
1.2 Sampling inspection 4
1.3 Properties of the curtailed inspection plan 7
1.4 Loss and risk functions 11
Problems 12
2 The sequential probability ratio test 15
2.1 Origin of the sprt 15
2.2 Derivation of the sprt 15
2.3 Some important properties of the sprt 18
2.4 Some applications of the sprt 24
Problems 30
3 Sequential tests between three hypotheses 35
3.1 Two examples 35
3.2 Formulation of the test 36
3.3 Properties of Sobel and Wald s test 39
3.4 Armitage s method 40
3.5 Billard and Vagholkar s test 43
3.6 Some special methods of treating three hypotheses 46
3.7 Application of the methods 47
Problems 48
4 Extensions to the SPRT 49
4.1 The problem of composite hypotheses 49
4.2 Wald s theory of weight functions 50
4.3 Some applications of Wald s theory of weight
functions 52
4.4 Transformation of observations 57
V
vi CONTENTS
4.5 Cox s theorem 58
4.6 Discussion 61
4.7 Asymptotic tests 62
Problems 66
5 Some applications of Cox s theorem 69
5.1 The sequential Mest 69
5.2 Two sided tests 70
5.3 Closed forms of the tests 73
5.4 Use of the tests 74
5.5 A sequential test of randomness 75
5.6 Sequential analysis of variance 80
5.7 Sequential X2 and t1 82
Problems 83
6 Some methods leading to closed boundaries 85
6.1 Review of Chapters 1 5 85
6.2 Armitage s restricted procedures 85
6.3 Approximate solution by diffusion theory 87
6.4 Application to tests for binomial probability 88
6.5 Contraction of the middle boundary 89
6.6 Boundaries to minimize the maximum expected
sample size 91
6.7 Discussion of Armitage s methods 91
Problems 94
7 Decision theory 97
7.1 Introduction 97
7.2 Decision theoretic approach to sampling
inspection 97
7.3 Bayesian approach 103
7.4 Design of a sequential sampling plan 108
7.5 Three terminal decisions 116
7.6 Empirical Bayes solutions 117
7.7 The minimax criterion 120
7.8 Discussion 124
Problems 125
8 Sequential estimation 129
8.1 Estimation versus hypothesis testing 129
8.2 Estimation 132
CONTENTS vii
8.3 Inverse binomial sampling 136
8.4 Asymptotic boundary theory 141
8.5 Bayesian decision theory approach to sequential
estimation 143
8.6 Discussion 149
8.7 Risk efficient estimators 150
8.8 Sequential interval estimation 151
8.9 Bayesian decision theory approach to sequential
interval estimation 155
Problems 157
9 Sequential estimation of points on regression functions 161
9.1 Introduction 161
9.2 The Robbins Monro process 162.
9.3 Dvoretzky s theorem 167
9.4 Practical use of the Robbins Monro process 169
9.5 The Kiefer Wolfowitz procedure 171
9.6 Methods for seeking the maximum of a response
surface 175
Problems 177
10 Sequential estimation of points on quantal response curves 181
10.1 Introduction 181
10.2 The Robbins Monro process 182
10.3 The up and down rule 185
10.4 Modifications to the up and down rule 189
10.5 Finite Markov chain approximation 191
10.6 Wetherill s udtr rule 194
Problems 198
11 Double sampling 199
11.1 Double sampling (sampling inspection) 199
11.2 Estimation by double sampling 201
11.3 Choice of the second sample size in double sampling 206
11.4 Stein s double sampling plan 208
Problems 210
12 Sequential allocation and selection problems 213
12.1 Bandit problems exploration versus exploitation 213
12.2 Adaptive allocation procedures for clinical trials 223
12.3 Allocation procedures to achieve balance 229
viii CONTENTS
12.4 Screening for drugs 231
12.5 Selection of the largest of k normal means 233
Problems 236
Appendix The normal diffusion process 239
References I General 241
II Applications 255
Author index 259
Subject index . 262
|
| adam_txt |
Contents
Preface Page ix
1 Introduction 1
1.1 Sequential experiments 1
1.2 Sampling inspection 4
1.3 Properties of the curtailed inspection plan 7
1.4 Loss and risk functions 11
Problems 12
2 The sequential probability ratio test 15
2.1 Origin of the sprt 15
2.2 Derivation of the sprt 15
2.3 Some important properties of the sprt 18
2.4 Some applications of the sprt 24
Problems 30
3 Sequential tests between three hypotheses 35
3.1 Two examples 35
3.2 Formulation of the test 36
3.3 Properties of Sobel and Wald's test 39
3.4 Armitage's method 40
3.5 Billard and Vagholkar's test 43
3.6 Some special methods of treating three hypotheses 46
3.7 Application of the methods 47
Problems 48
4 Extensions to the SPRT 49
4.1 The problem of composite hypotheses ' 49
4.2 Wald's theory of weight functions 50
4.3 Some applications of Wald's theory of weight
functions 52
4.4 Transformation of observations 57
V
vi CONTENTS
4.5 Cox's theorem 58
4.6 Discussion 61
4.7 Asymptotic tests 62
Problems 66
5 Some applications of Cox's theorem 69
5.1 The sequential Mest 69
5.2 Two sided tests 70
5.3 Closed forms of the tests 73
5.4 Use of the tests 74
5.5 A sequential test of randomness 75
5.6 Sequential analysis of variance 80
5.7 Sequential X2 and t1 82
Problems 83
6 Some methods leading to closed boundaries 85
6.1 Review of Chapters 1 5 85
6.2 Armitage's 'restricted' procedures 85
6.3 Approximate solution by diffusion theory 87
6.4 Application to tests for binomial probability 88
6.5 Contraction of the middle boundary 89
6.6 Boundaries to minimize the maximum expected
sample size 91
6.7 Discussion of Armitage's methods 91
Problems 94
7 Decision theory 97
7.1 Introduction 97
7.2 Decision theoretic approach to sampling
inspection 97
7.3 Bayesian approach 103
7.4 Design of a sequential sampling plan 108
7.5 Three terminal decisions 116
7.6 Empirical Bayes solutions 117
7.7 The minimax criterion 120
7.8 Discussion 124
Problems 125
8 Sequential estimation 129
8.1 Estimation versus hypothesis testing 129
8.2 Estimation 132
CONTENTS vii
8.3 Inverse binomial sampling 136
8.4 Asymptotic boundary theory 141
8.5 Bayesian decision theory approach to sequential
estimation 143
8.6 Discussion 149
8.7 Risk efficient estimators 150
8.8 Sequential interval estimation 151
8.9 Bayesian decision theory approach to sequential
interval estimation 155
Problems 157
9 Sequential estimation of points on regression functions 161
9.1 Introduction 161
9.2 The Robbins Monro process 162.
9.3 Dvoretzky's theorem 167
9.4 Practical use of the Robbins Monro process 169
9.5 The Kiefer Wolfowitz procedure 171
9.6 Methods for seeking the maximum of a response
surface 175
Problems 177
10 Sequential estimation of points on quantal response curves 181
10.1 Introduction 181
10.2 The Robbins Monro process 182
10.3 The up and down rule 185
10.4 Modifications to the up and down rule 189
10.5 Finite Markov chain approximation 191
10.6 Wetherill's udtr rule 194
Problems 198
11 Double sampling 199
11.1 Double sampling (sampling inspection) 199
11.2 Estimation by double sampling 201
11.3 Choice of the second sample size in double sampling 206
11.4 Stein's double sampling plan 208
Problems 210
12 Sequential allocation and selection problems 213
12.1 Bandit problems exploration versus exploitation 213
12.2 Adaptive allocation procedures for clinical trials 223
12.3 Allocation procedures to achieve balance 229
viii CONTENTS
12.4 Screening for drugs 231
12.5 Selection of the largest of k normal means 233
Problems 236
Appendix The normal diffusion process 239
References I General 241
II Applications 255
Author index 259
Subject index . 262 |
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| spelling | Wetherill, George Barrie 1932- Verfasser (DE-588)135980038 aut Sequential methods in statistics G. Barrie Wetherill ; Kevin D. Glazebrook 3. ed. London [u.a.] Chapman and Hall 1986 XI, 264 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability Sequentiële analyse (statistiek) gtt Statistiek gtt Statistik Sequential analysis Sequentialanalyse (DE-588)4128461-6 gnd rswk-swf Sequentialmethode (DE-588)4301567-0 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Sequentialanalyse (DE-588)4128461-6 s DE-604 Sequentialmethode (DE-588)4301567-0 s Statistik (DE-588)4056995-0 s 1\p DE-604 Glazebrook, Kevin D. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015088830&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wetherill, George Barrie 1932- Glazebrook, Kevin D. Sequential methods in statistics Sequentiële analyse (statistiek) gtt Statistiek gtt Statistik Sequential analysis Sequentialanalyse (DE-588)4128461-6 gnd Sequentialmethode (DE-588)4301567-0 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4128461-6 (DE-588)4301567-0 (DE-588)4056995-0 |
| title | Sequential methods in statistics |
| title_auth | Sequential methods in statistics |
| title_exact_search | Sequential methods in statistics |
| title_exact_search_txtP | Sequential methods in statistics |
| title_full | Sequential methods in statistics G. Barrie Wetherill ; Kevin D. Glazebrook |
| title_fullStr | Sequential methods in statistics G. Barrie Wetherill ; Kevin D. Glazebrook |
| title_full_unstemmed | Sequential methods in statistics G. Barrie Wetherill ; Kevin D. Glazebrook |
| title_short | Sequential methods in statistics |
| title_sort | sequential methods in statistics |
| topic | Sequentiële analyse (statistiek) gtt Statistiek gtt Statistik Sequential analysis Sequentialanalyse (DE-588)4128461-6 gnd Sequentialmethode (DE-588)4301567-0 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Sequentiële analyse (statistiek) Statistiek Statistik Sequential analysis Sequentialanalyse Sequentialmethode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015088830&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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