Introduction to nonparametric estimation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
New York
Springer
[2009]
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xii, 214 Seiten Diagramme |
| ISBN: | 9780387790510 9781441927095 |
Internformat
MARC
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| 100 | 1 | |a Cybakov, Aleksandr B. |e Verfasser |0 (DE-588)111180600 |4 aut | |
| 240 | 1 | 0 | |a Introduction à l'estimation non-paramétrique |
| 245 | 1 | 0 | |a Introduction to nonparametric estimation |c Alexandre B. Tsybakov |
| 264 | 1 | |a New York |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
NONPARAMETRIC ESTIMATORS 1
1.1 EXAMPLES OF NONPARAMETRIC MODELS AND PROBLEMS 1
1.2 KERNEL DENSITY ESTIMATORS 2
1.2.1 MEAN SQUARED ERROR OF KERNEL ESTIMATORS 4
1.2.2 CONSTRUCTION OF A KERNEL OF ORDER 10
1.2.3 INTEGRATED SQUARED RISK OF KERNEL ESTIMATORS 12
1.2.4 LACK OF ASYMPTOTIC OPTIMALITY FOR FIXED DENSITY 16
1.3 FOURIER ANALYSIS OF KERNEL DENSITY ESTIMATORS 19
1.4 UNBIASED RISK ESTIMATION. CROSS-VALIDATION DENSITY ESTIMATORS . 27
1.5 NONPARAMETRIC REGRESSION. THE NADARAYA-WATSON ESTIMATOR. 31 1.6
LOCAL POLYNOMIAL ESTIMATORS 34
1.6.1 POINTWISE AND INTEGRATED RISK OF LOCAL POLYNOMIAL ESTIMATORS 37
1.6.2 CONVERGENCE IN THE SUP-NORM 42
1.7 PROJECTION ESTIMATORS 46
1.7.1 SOBOLEV CLASSES AND ELLIPSOIDS 49
1.7.2 INTEGRATED SQUARED RISK OF PROJECTION ESTIMATORS 51
1.7.3 GENERALIZATIONS 57
1.8 ORACLES 59
1.9 UNBIASED RISK ESTIMATION FOR REGRESSION 61
1.10 THREE GAUSSIAN MODELS 65
1.11 NOTES 69
1.12 EXERCISES 72
LOWER BOUNDS ON THE MINIMAX RISK 77
2.1 INTRODUCTION 77
2.2 A GENERAL REDUCTION SCHEME 79
2.3 LOWER BOUNDS BASED ON TWO HYPOTHESES 81
2.4 DISTANCES BETWEEN PROBABILITY MEASURES 83
2.4.1 INEQUALITIES FOR DISTANCES 86
2.4.2 BOUNDS BASED ON DISTANCES 90
IMAGE 2
2.5 LOWER BOUNDS ON THE RISK OF REGRESSION ESTIMATORS AT A POINT . . 91
2.6 LOWER BOUNDS BASED ON MANY HYPOTHESES 95
2.6.1 LOWER BOUNDS IN LI 102
2.6.2 LOWER BOUNDS IN THE SUP-NORM 108
2.7 OTHER TOOLS FOR MINIMAX LOWER BOUNDS 110
2.7.1 FANO'S LEMMA 110
2.7.2 ASSOUAD'S LEMMA 116
2.7.3 THE VAN TREES INEQUALITY 120
2.7.4 THE METHOD OF TWO FUZZY HYPOTHESES 125
2.7.5 LOWER BOUNDS FOR ESTIMATORS OF A QUADRATIC FUNCTIONAL. . 128 2.8
NOTES 131
2.9 EXERCISES 133
3 ASYMPTOTIC EFFICIENCY AND ADAPTATION 137
3.1 PINSKER'S THEOREM 137
3.2 LINEAR MINIMAX LEMMA 140
3.3 PROOF OF PINSKER'S THEOREM 146
3.3.1 UPPER BOUND ON THE RISK 146
3.3.2 LOWER BOUND ON THE MINIMAX RISK 147
3.4 STEIN'S PHENOMENON 155
3.4.1 STEIN'S SHRINKAGE AND THE JAMES-STEIN ESTIMATOR 157 3.4.2 OTHER
SHRINKAGE ESTIMATORS 162
3.4.3 SUPEREFFICIENCY 165
3.5 UNBIASED ESTIMATION OF THE RISK 166
3.6 ORACLE INEQUALITIES 174
3.7 MINIMAX ADAPTIVITY 179
3.8 INADMISSIBILITY OF THE PINSKER ESTIMATOR 180
3.9 NOTES 185
3.10 EXERCISES 187
APPENDIX 191
BIBLIOGRAPHY 203
INDEX 211 |
| any_adam_object | 1 |
| author | Cybakov, Aleksandr B. |
| author_GND | (DE-588)111180600 |
| author_facet | Cybakov, Aleksandr B. |
| author_role | aut |
| author_sort | Cybakov, Aleksandr B. |
| author_variant | a b c ab abc |
| building | Verbundindex |
| bvnumber | BV035403501 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.8 |
| callnumber-search | QA278.8 |
| callnumber-sort | QA 3278.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 SK 830 SK 835 |
| classification_tum | MAT 626f |
| ctrlnum | (OCoLC)244765632 (DE-599)DNB989740293 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| isbn | 9780387790510 9781441927095 |
| language | English French |
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| spelling | Cybakov, Aleksandr B. Verfasser (DE-588)111180600 aut Introduction à l'estimation non-paramétrique Introduction to nonparametric estimation Alexandre B. Tsybakov New York Springer [2009] © 2009 xii, 214 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Hier auch später erschienene, unveränderte Nachdrucke Estimation theory Nonparametric statistics Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Dichteschätzung (DE-588)4353528-8 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Nichtparametrische Schätzung (DE-588)4203980-0 s Dichteschätzung (DE-588)4353528-8 s Asymptotik (DE-588)4126634-1 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-79052-7 Erweiterte Ausgabe von Introduction à l'estimation non-paramétrique (DE-604)BV025504210 Übersetzung von Introduction à l'estimation non-paramétrique (DE-604)BV025504210 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3140260&prov=M&dok_var=1&dok_ext=htm Inhaltstext SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017324107&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cybakov, Aleksandr B. Introduction to nonparametric estimation Estimation theory Nonparametric statistics Nichtparametrische Schätzung (DE-588)4203980-0 gnd Dichteschätzung (DE-588)4353528-8 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4203980-0 (DE-588)4353528-8 (DE-588)4126634-1 (DE-588)4123623-3 |
| title | Introduction to nonparametric estimation |
| title_alt | Introduction à l'estimation non-paramétrique |
| title_auth | Introduction to nonparametric estimation |
| title_exact_search | Introduction to nonparametric estimation |
| title_full | Introduction to nonparametric estimation Alexandre B. Tsybakov |
| title_fullStr | Introduction to nonparametric estimation Alexandre B. Tsybakov |
| title_full_unstemmed | Introduction to nonparametric estimation Alexandre B. Tsybakov |
| title_short | Introduction to nonparametric estimation |
| title_sort | introduction to nonparametric estimation |
| topic | Estimation theory Nonparametric statistics Nichtparametrische Schätzung (DE-588)4203980-0 gnd Dichteschätzung (DE-588)4353528-8 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Estimation theory Nonparametric statistics Nichtparametrische Schätzung Dichteschätzung Asymptotik Lehrbuch |
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