Empirical Bayes methods:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Chapman and Hall
1989
|
| Edition: | 2. ed. |
| Series: | Monographs on statistics and applied probability
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 284 S. |
| ISBN: | 0412277603 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Acknowledgements viii
Preface ix
Notation and abbreviations xi
1 Introduction to Bayes and empirical Bayes methods 1
1.1 The problem, Bayes conventional and empirical Bayes
methods 1
1.2 An introduction to Bayes techniques 3
1.3 Bayes point estimation: one parameter 4
1.4 Bayes decisions between k simple hypotheses 8
1.5 Bayes decisions between two composite hypotheses 9
1.6 Bayes estimation of vector parameters 11
1.7 Bayes decisions and multiple independent observations 12
1.8 Empirical Bayes methods 13
1.9 An example: EB estimation in the Poisson case 14
1.10 The goodness of EB procedures 16
1.11 Smooth EB estimates 17
1.12 Approximate Bayes and empirical Bayes methods 18
1.13 Concomitant variables 21
1.14 Competitors of EB methods 21
2 Estimation of the prior distribution 27
2.1 Introduction 27
2.2 Identifiability 28
2.3 Parametric G families 29
2.4 Finite mixtures 31
2.5 General mixtures: identifiability 37
2.6 Identifiability of multiparameter mixtures 41
2.7 Determination of G(JS) 44
2.8 Estimation of G: parametric G families 49
vi CONTENTS
2.9 Estimation of G: finite approximation of G 54
2.10 Estimation of G: continuous mixtures 56
2.11 Estimation of G: miscellaneous methods 58
2.12 Estimation with unequal component sample sizes 59
3 Empirical Bayes point estimation 64
3.1 Introduction 64
3.2 Asymptotic optimality 65
3.3 Robustness with respect to the prior distribution 68
3.4 Simple EB estimates 71
3.5 EB estimation through estimating G 78
3.6 Linear EB estimation 83
3.7 EB estimation for special univariate distributions: one
current observation 84
3.8 EB estimation with multiple current observations: one
parameter 92
3.9 Unequal mt 1: application to particular distributions 98
3.10 Nonparametric EB estimation 105
3.11 Assessing performance of EBEs in practice 112
4 Empirical Bayes point estimation: vector parameters 118
4.1 Introduction 118
4.2 Location scale estimation 118
4.3 Quantile estimation 128
4.4 The multivariate normal distribution 131
4.5 The multinomial distribution 140
4.6 Linear Bayes and EB, and subsets of parameters 146
4.7 Concomitant variables 149
5 Testing of hypotheses 152 (
5.1 Introduction 152
5.2 Two simple hypotheses, one parameter problems 153
5.3 k ^ 3 simple hypotheses 161
5.4 Two composite hypotheses 164
6 Bayes and empirical Bayes interval estimation 173
6.1 Introduction 173
6.2 Intervals for single parameters 173
6.3 The multiparameter case: region estimators 186
6.4 Bayes statistical tolerance regions 191
]
t
CONTENTS vii
6.5 EB tolerance regions 196
6.6 Other approaches to EB interval and region
estimation 200
7 Alternatives to empirical Bayes 205
7.1 Introduction 205
7.2 The multiparameter full Bayesian approach 205
7.3 Likelihood based approaches 211
7.4 Compound estimation and decision theory 216
7.5 General discussion 240
8 Applications of EB methods 242
8.1 Introduction 242
8.2 Examples with normal data distributions 243
8.3 Examples involving standard discrete distributions 251
8.4 Miscellaneous EB applications 263
References 272
Author index 280
Subject index 282
|
| any_adam_object | 1 |
| author | Maritz, Johannes Stephanus 1928- Lwin, Thaung 1944- |
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| author_facet | Maritz, Johannes Stephanus 1928- Lwin, Thaung 1944- |
| author_role | aut aut |
| author_sort | Maritz, Johannes Stephanus 1928- |
| author_variant | j s m js jsm t l tl |
| building | Verbundindex |
| bvnumber | BV002499797 |
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| classification_tum | MAT 622f |
| ctrlnum | (OCoLC)246555578 (DE-599)BVBBV002499797 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T15:45:57Z |
| institution | BVB |
| isbn | 0412277603 |
| language | English |
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| physical | X, 284 S. |
| publishDate | 1989 |
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| series2 | Monographs on statistics and applied probability |
| spelling | Maritz, Johannes Stephanus 1928- Verfasser (DE-588)172249163 aut Empirical Bayes methods J. S. Maritz and T. Lwin 2. ed. London u.a. Chapman and Hall 1989 X, 284 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 35 Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf CD-ROM (DE-588)4139307-7 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayer-Verfahren (DE-588)4210428-2 gnd rswk-swf Methode (DE-588)4038971-6 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s DE-604 Inferenzstatistik (DE-588)4247120-5 s Methode (DE-588)4038971-6 s Bayes-Entscheidungstheorie (DE-588)4144220-9 s CD-ROM (DE-588)4139307-7 s Bayer-Verfahren (DE-588)4210428-2 s 1\p DE-604 Lwin, Thaung 1944- Verfasser (DE-588)172234131 aut Monographs on statistics and applied probability 35 (DE-604)BV002494005 35 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001610328&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 | Maritz, Johannes Stephanus 1928- Lwin, Thaung 1944- Empirical Bayes methods Monographs on statistics and applied probability Bayes-Verfahren (DE-588)4204326-8 gnd Inferenzstatistik (DE-588)4247120-5 gnd CD-ROM (DE-588)4139307-7 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Bayer-Verfahren (DE-588)4210428-2 gnd Methode (DE-588)4038971-6 gnd |
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| title | Empirical Bayes methods |
| title_auth | Empirical Bayes methods |
| title_exact_search | Empirical Bayes methods |
| title_full | Empirical Bayes methods J. S. Maritz and T. Lwin |
| title_fullStr | Empirical Bayes methods J. S. Maritz and T. Lwin |
| title_full_unstemmed | Empirical Bayes methods J. S. Maritz and T. Lwin |
| title_short | Empirical Bayes methods |
| title_sort | empirical bayes methods |
| topic | Bayes-Verfahren (DE-588)4204326-8 gnd Inferenzstatistik (DE-588)4247120-5 gnd CD-ROM (DE-588)4139307-7 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Bayer-Verfahren (DE-588)4210428-2 gnd Methode (DE-588)4038971-6 gnd |
| topic_facet | Bayes-Verfahren Inferenzstatistik CD-ROM Bayes-Entscheidungstheorie Bayer-Verfahren Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001610328&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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