Inference and asymptotics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Chapman & Hall
1994
|
| Edition: | 1. ed. |
| Series: | Monographs on statistics and applied probability
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [332] - 349 |
| Physical Description: | X, 360 S. Illustrationen |
| ISBN: | 041249440X |
Staff View
MARC
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| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1994 | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
1 Preliminaries 1
1.1 Introduction 1
1.2 Normal theory linear model 3
1.3 Exponential models 4
1.4 Transformation models 8
1.5 Invariance 10
Further results and exercises 11
Bibliographic notes 13
2 Some general concepts 14
2.1 Introduction 14
2.2 Likelihood 14
2.3 Sufficiency 28
2.4 Conditioning and some general concepts 32
2.5 Ancillarity 36
2.6 Examination of model adequacy 45
2.7 Parameter orthogonality 49
2.8 Review of transformation models 52
2.9 Review of prime exponential models 61
2.10 Review of curved exponential models 65
Further results and exercises 72
Bibliographic notes 78
3 First-order theory 80
3.1 Introduction 80
3.2 Main statistics: no nuisance parameters 80
3.3 Distribution theory: no nuisance parameters 85
3.4 Profile likelihood 89
3.5 Further statistics: nuisance parameter case 91
vi CONTENTS
3.6 Effects of parameter orthogonality 98
3.7 Distribution theory: nuisance parameter case 100
3.8 Non-standard cases 106
Further results and exercises 111
Bibliographic notes 117
4 Higher-order theory: preliminaries and motivations 119
4.1 Introduction 119
4.2 Choice between different statistics: qualitative
considerations 119
4.3 The reasons for modifying simple likelihood-based
methods 123
4.4 Higher-order theory: the key questions 131
Further results and exercises 139
Bibliographic notes 141
5 Some tools of higher-order theory 143
5.1 Introduction 143
5.2 Log-likelihood derivatives and mixed log model
derivatives 145
5.3 Expansion of likelihood quantities:
expected/observed case 148
5.4 Expansion of likelihood quantities: observed case 155
5.5 Translation between observed and expected
expressions 157
5.6 Yokes and invariant calculations 161
5.7 Appendix: Differentiation of matrix quantities 168
Further results and exercises 169
Bibliographic notes 170
6 Higher-order theory: likelihood combinants 172
6.1 Introduction 172
6.2 The p*-formula 173
6.3 The score and the profile score 179
6.4 The maximum likelihood estimator revisited 184
6.5 The likelihood ratio 188
6.6 The directed likelihood 201
6.7 Approximate interval probabilities 211
Further results and exercises 217
Bibliographic notes 222
CONTENTS vii
7 Higher-order theory: some further results and tools 225
7.1 Introduction 225
7.2 Approximate sufficiency and ancillarity 225
7.3 Jacobians of conditionality structures 236
7.4 Derivation of p+ and p* for curved exponential
models 238
7.5 The effect of sampling rules 240
7.6 Independence of second order 251
Further results and exercises 255
Bibliographic notes 259
8 Various notions of pseudo-likelihood and higher-order
theory 261
8.1 Introduction 261
8.2 Modified profile likelihood 263
8.3 Stable adjustments of profile likelihood 269
8.4 Stable adjustments of directed likelihood 274
8.5 Large number of nuisance parameters 282
8.6 Further definitions of pseudo-likelihood 289
Further results and exercises 294
Bibliographic notes 296
9 Further aspects 298
9.1 Pivots 298
9.2 Estimating equations and quasi-likelihood 301
9.3 Stochastic processes and time series 306
9.4 Prediction 314
9.5 Asymptotic randomization theory 320
Further results and exercises 327
Bibliographic notes 330
References 332
Author index 351
Subject index 354
Contents
Preface ix
1 Preliminaries 1
1.1 Introduction 1
1.2 Normal theory linear model 3
1.3 Exponential models 4
1.4 Transformation models 8
1.5 Invariance 10
Further results and exercises 11
Bibliographic notes 13
2 Some general concepts 14
2.1 Introduction 14
2.2 Likelihood 14
2.3 Sufficiency 28
2.4 Conditioning and some general concepts 32
2.5 Ancillarity 36
2.6 Examination of model adequacy 45
2.7 Parameter orthogonality 49
2.8 Review of transformation models 52
2.9 Review of prime exponential models 61
2.10 Review of curved exponential models 65
Further results and exercises 72
Bibliographic notes 78
3 First order theory 80
3.1 Introduction 80
3.2 Main statistics: no nuisance parameters 80
3.3 Distribution theory: no nuisance parameters 85
3.4 Profile likelihood 89
3.5 Further statistics: nuisance parameter case 91
vi CONTENTS
3.6 Effects of parameter orthogonality 98
3.7 Distribution theory: nuisance parameter case 100
3.8 Non standard cases 106
Further results and exercises 111
Bibliographic notes 117
4 Higher order theory: preliminaries and motivations 119
4.1 Introduction 119
4.2 Choice between different statistics: qualitative
considerations 119
4.3 The reasons for modifying simple likelihood based
methods 123
4.4 Higher order theory: the key questions 131
Further results and exercises 139
Bibliographic notes 141
5 Some tools of higher order theory 143
5.1 Introduction 143
5.2 Log likelihood derivatives and mixed log model
derivatives 145
5.3 Expansion of likelihood quantities:
expected/observed case 148
5.4 Expansion of likelihood quantities: observed case 155
5.5 Translation between observed and expected
expressions 157
5.6 Yokes and invariant calculations 161
5.7 Appendix: Differentiation of matrix quantities 168
Further results and exercises 169
Bibliographic notes 170
6 Higher order theory: likelihood combinants 172
6.1 Introduction 172
6.2 The p* formula 173
6.3 The score and the profile score 179
6.4 The maximum likelihood estimator revisited 184
6.5 The likelihood ratio 188
6.6 The directed likelihood 201
6.7 Approximate interval probabilities 211
Further results and exercises 217
Bibliographic notes 222
CONTENTS vii
7 Higher order theory: some further results and tools 225
7.1 Introduction 225
7.2 Approximate sufficiency and ancillarity 225
7.3 Jacobians of conditionality structures 236
7.4 Derivation of p+ and p* for curved exponential
models 238
7.5 The effect of sampling rules 240
7.6 Independence of second order 251
Further results and exercises 255
Bibliographic notes 259
8 Various notions of pseudo likelihood and higher order
theory 261
8.1 Introduction 261
8.2 Modified profile likelihood 263
8.3 Stable adjustments of profile likelihood 269
8.4 Stable adjustments of directed likelihood 274
8.5 Large number of nuisance parameters 282
8.6 Further definitions of pseudo likelihood 289
Further results and exercises 294
Bibliographic notes 296
9 Further aspects 298
9.1 Pivots 298
9.2 Estimating equations and quasi likelihood 301
9.3 Stochastic processes and time series 306
9.4 Prediction 314
9.5 Asymptotic randomization theory 320
Further results and exercises 327
Bibliographic notes 330
References 332
Author index 351
Subject index 354
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| isbn | 041249440X |
| language | English |
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| spelling | Barndorff-Nielsen, Ole E. 1935- Verfasser (DE-588)123060915 aut Inference and asymptotics O. E. Barndorff-Nielsen and D. R. Cox 1. ed. London [u.a.] Chapman & Hall 1994 X, 360 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 52 Literaturverz. S. [332] - 349 Non-parametrische statistiek gtt Statistique mathématique - Théorie asymptotique ram Statistik Mathematical statistics Asymptotic theory Models, Statistical Statistics Asymptotische Statistik (DE-588)4203167-9 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Asymptotische Statistik (DE-588)4203167-9 s DE-604 Statistische Schlussweise (DE-588)4182963-3 s DE-188 Cox, David R. 1924-2022 Verfasser (DE-588)119013169 aut Monographs on statistics and applied probability 52 (DE-604)BV002494005 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006458494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006458494&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barndorff-Nielsen, Ole E. 1935- Cox, David R. 1924-2022 Inference and asymptotics Monographs on statistics and applied probability Non-parametrische statistiek gtt Statistique mathématique - Théorie asymptotique ram Statistik Mathematical statistics Asymptotic theory Models, Statistical Statistics Asymptotische Statistik (DE-588)4203167-9 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4203167-9 (DE-588)4182963-3 |
| title | Inference and asymptotics |
| title_auth | Inference and asymptotics |
| title_exact_search | Inference and asymptotics |
| title_full | Inference and asymptotics O. E. Barndorff-Nielsen and D. R. Cox |
| title_fullStr | Inference and asymptotics O. E. Barndorff-Nielsen and D. R. Cox |
| title_full_unstemmed | Inference and asymptotics O. E. Barndorff-Nielsen and D. R. Cox |
| title_short | Inference and asymptotics |
| title_sort | inference and asymptotics |
| topic | Non-parametrische statistiek gtt Statistique mathématique - Théorie asymptotique ram Statistik Mathematical statistics Asymptotic theory Models, Statistical Statistics Asymptotische Statistik (DE-588)4203167-9 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Non-parametrische statistiek Statistique mathématique - Théorie asymptotique Statistik Mathematical statistics Asymptotic theory Models, Statistical Statistics Asymptotische Statistik Statistische Schlussweise |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006458494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006458494&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT barndorffnielsenolee inferenceandasymptotics AT coxdavidr inferenceandasymptotics |
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