Parametric statistical theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
<<de>> Gruyter
1994
|
| Series: | De Gruyter textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [345] - 359 |
| Physical Description: | XIII, 374 S. graph. Darst. |
| ISBN: | 3110138638 3110140306 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface v
Introduction vii
Chapter 1 Sufficiency and completeness 1
1.1 Introduction 1
1.2 Sufficiency and factorization of densities 4
1.3 Sufficiency and exhaustivity 8
1.4 Minimal sufficiency 12
1.5 Completeness 17
1.6 Exponential families 22
1.7 Auxiliary results on families with monotone likelihood ratios 31
1.8 Ancillary statistics 44
1.9 Equivariance and invariance 49
1.10 Appendix: Conditional expectations, conditional distributions 55
Chapter 2 The evaluation of estimators 65
2.1 Introduction 65
2.2 Unbiasedness of estimators 68
2.3 The concentration of real valued estimators 74
2.4 Concentration of multivariate estimators 82
2.5 Evaluating estimators by loss functions 90
2.6 The relative efficiency of estimators 93
2.7 Examples on the evaluation of estimators 95
Chapter 3 Mean unbiased estimators and convex loss
functions 101
3.1 Introduction 101
3.2 The Rao Blackwell Lehmann Scheffe Theorem 104
3.3 Examples of mean unbiased estimators with minimal
convex risk 109
3.4 Mean unbiased estimation of probabilities 112
3.5 A result on bounded mean unbiased estimators 120
xii Contents
Chapter 4 Testing hypotheses 123
4.1 Basic concepts 123
4.2 Critical functions, critical regions 128
4.3 The Neyman Pearson Lemma 133
4.4 Optimal tests for composite hypotheses 135
4.5 Optimal tests for families with monotone likelihood ratios 139
4.6 Tests of Neyman structure 143
4.7 Most powerful similar tests for a real parameter
in the presence of a nuisance parameter 146
Chapter 5 Confidence procedures 157
5.1 Basic concepts 157
5.2 The evaluation of confidence procedures 160
5.3 The construction of one sided confidence bounds and
median unbiased estimators 167
5.4 Optimal one sided confidence bounds and median unbiased
estimators 171
5.5 Optimal one sided confidence bounds and median unbiased
estimators in the presence of a nuisance parameter 174
5.6 Examples of maximally concentrated confidence bounds 180
Chapter 6 Consistent estimators 187
6.1 Introduction 187
6.2 A general consistency theorem 189
6.3 Consistency of M estimators 193
6.4 Consistent solutions of estimating equations 200
6.5 Consistency of maximum likelihood estimators 203
6.6 Examples of ML estimators 209
6.7 Appendix: Uniform integrability, stochastic convergence and
measurable selection 213
Chapter 7 Asymptotic distributions of estimator sequences 225
7.1 Limit distributions 225
7.2 How to deal with limit distributions 231
7.3 Asymptotic confidence bounds 236
7.4 Solutions to estimating equations 240
7.5 The limit distribution of ML estimator sequences 247
7.6 Stochastic approximations to estimator sequences 251
7.7 Appendix: Weak convergence 255
Contents xiii
Chapter 8 Asymptotic bounds for the concentration of
estimators and confidence bounds 263
8.1 Introduction 263
8.2 Regular sequences of confidence bounds and
median unbiased estimators 269
8.3 Sequences of confidence bounds and median unbiased
estimators with limit distributions 276
8.4 The convolution theorem 278
8.5 Maximally concentrated limit distributions 288
8.6 Superefficiency 296
Chapter 9 Miscellaneous results on asymptotic distributions 305
9.1 Examples of ML estimators 305
9.2 Tolerance bounds 316
9.3 Probability measures with location and scale parameters 320
9.4 Miscellaneous results on estimators 332
Chapter 10 Asymptotic test theory 337
10.1 Introduction 337
10.2 Tests for a real valued functional 338
10.3 The asymptotic envelope power function for tests for
a real valued functional 341
References 345
Author Index 361
Subject Index 365
Notation Index 371
|
| any_adam_object | 1 |
| author | Pfanzagl, Johann 1928-2019 |
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| ctrlnum | (OCoLC)30594330 (DE-599)BVBBV009686531 |
| dewey-full | 519.5/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/4 |
| dewey-search | 519.5/4 |
| dewey-sort | 3519.5 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009686531 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:39:12Z |
| institution | BVB |
| isbn | 3110138638 3110140306 |
| language | English |
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| physical | XIII, 374 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series2 | De Gruyter textbook |
| spelling | Pfanzagl, Johann 1928-2019 Verfasser (DE-588)135982200 aut Parametric statistical theory Johann Pfanzagl Berlin u.a. <<de>> Gruyter 1994 XIII, 374 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Literaturverz. S. [345] - 359 Statistiek gtt Statistique mathématique ram Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Parameterschätzung (DE-588)4044614-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006406029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pfanzagl, Johann 1928-2019 Parametric statistical theory Statistiek gtt Statistique mathématique ram Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4044614-1 |
| title | Parametric statistical theory |
| title_auth | Parametric statistical theory |
| title_exact_search | Parametric statistical theory |
| title_full | Parametric statistical theory Johann Pfanzagl |
| title_fullStr | Parametric statistical theory Johann Pfanzagl |
| title_full_unstemmed | Parametric statistical theory Johann Pfanzagl |
| title_short | Parametric statistical theory |
| title_sort | parametric statistical theory |
| topic | Statistiek gtt Statistique mathématique ram Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Statistiek Statistique mathématique Statistik Mathematical statistics Parameterschätzung |
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