Likelihood methods in statistics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Edition: | Reprint. |
| Series: | Oxford statistical science series
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 380 S. graph. Darst. |
| ISBN: | 9780198506508 |
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MARC
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| 245 | 1 | 0 | |a Likelihood methods in statistics |c Thomas A. Severini |
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Record in the Search Index
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| adam_text | Titel: Likelihood methods in statistics
Autor: Severini, Thomas A
Jahr: 2008
Likelihood Methods in Statistics
THOMAS A. SEVERINI
Department of Statistics
Northwestern University
Evanston, Illinois
OXFORD
UNIVERSITY PRESS
Contents
1 Some basic concepts 1
1.1 Introduction 1
1.2 Exponential family modeis 4
1.3 Transformation modeis 7
1.4 Cumulants 11
1.5 Sufficiency 16
1.6 AnciDary statistics 19
1.7 Normal distribution theory 22
1.8 Discussion and references 23
1.9 Exercises 24
2 Large-sample approximations 27
2.1 Introduction 27
2.2 Central limit theorem 28
2.3 Edgeworth series approximations 31
2.4 Saddlepoint approximation of densities 37
2.5 Approximation of integrals and sums 40
2.6 Saddlepoint approximations for distribution functions 46
2.7 Saddlepoint approximations for lattice variables 49
2.8 Saddlepoint approximations for multivariate
distributions 53
2.9 Stochastic asymptotic expansions 54
2.10 Approximation of conditional distributions 58
2.11 Laplace approximations 66
2.12 Discussion and references 68
2.13 Exercises 69
3 Likelihood 73
3.1 Introduction 73
3.2 Some properties of the likelihood function 75
3.3 The likelihood principle 77
3.4 Regulär modeis 80
3.5 Log-likelihood derivatives 85
3.6 Information 88
3.7 Methods of inference 96
3.8 Discussion and references 100
3.9 Exercises 102
X CONTENTS
First-order asymptotic theory 105
4.1 Introduction 105
4.2 Maximum likelihood estimates 105
4.3 The likelihood ratio statistic 113
4.4 The score and Wald statistics 120
4.5 Confidence regions 123
4.6 The profile likelihood function 126
4.7 Nonregular modeis 129
4.8 Discussion and references 133
4.9 Exercises 134
Higher-order asymptotic theory 138
5.1 Introduction 138
5.2 Some preliminary results 138
5.3 Maximum likelihood estimates 141
5.4 Likelihood ratio statistic 154
5.5 Saddlepoint approximations 163
5.6 Discussion and references 171
5.7 Exercises 172
Asymptotic theory and conditional inference 175
6.1 Introduction 175
6.2 Log-likelihood derivatives 176
6.3 Conditional distribution of maximum likelihood
estimates 183
6.4 Stahle inference 196
6.5 Approximation of the conditional model 204
6.6 Approximate ancillarity 209
6.7 Approximation of sample space derivatives 218
6.8 Discussion and references 234
6.9 Exercises 235
The signed likelihood ratio statistic 238
7.1 Introduction 238
7.2 Normalizing transformations 239
7.3 One-parameter modeis 241
7.4 Scalar parameter of interest in the presence of a
nuisance parameter 248
7.5 Approximations to R* 261
7.6 Discussion and references 274
7.7 Exercises 275
Likelihood functions for a parameter of interest 278
8.1 Introduction 278
8.2 Conditional likelihood functions 279
8.3 Marginal likelihood functions 298
8.4 Integrated likelihood functions 306
CONTENTS XI
8.5 Inference based on a pseudo-likelihood function 309
8.6 Discussion and references 319
8.7 Exercises 320
The modified profile likelihood function 323
9.1 Introduction 323
9.2 Profile likelihood 323
9.3 Modified profile likelihood 327
9.4 Calculation of the modified profile likelihood without
an explicit nuisance paramter 337
9.5 Approximations to the modified profile likelihood 340
9.6 Discussion and references 352
9.7 Exercises 352
Appendix: Data sets used in the examples 354
References 362
Author index 374
Subject index 377
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:09:35Z |
| institution | BVB |
| isbn | 9780198506508 |
| language | English |
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| publishDate | 2008 |
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| spelling | Severini, Thomas A. Verfasser aut Likelihood methods in statistics Thomas A. Severini Reprint. Oxford [u.a.] Oxford Univ. Press 2008 XI, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford statistical science series 22 Statistiek gtt Waarschijnlijkheidstheorie gtt Statistik Estimation theory Schätztheorie (DE-588)4121608-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 s DE-604 Oxford statistical science series 22 (DE-604)BV001908661 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024564258&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Severini, Thomas A. Likelihood methods in statistics Oxford statistical science series Statistiek gtt Waarschijnlijkheidstheorie gtt Statistik Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4121608-8 |
| title | Likelihood methods in statistics |
| title_auth | Likelihood methods in statistics |
| title_exact_search | Likelihood methods in statistics |
| title_full | Likelihood methods in statistics Thomas A. Severini |
| title_fullStr | Likelihood methods in statistics Thomas A. Severini |
| title_full_unstemmed | Likelihood methods in statistics Thomas A. Severini |
| title_short | Likelihood methods in statistics |
| title_sort | likelihood methods in statistics |
| topic | Statistiek gtt Waarschijnlijkheidstheorie gtt Statistik Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Statistiek Waarschijnlijkheidstheorie Statistik Estimation theory Schätztheorie |
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