Hilbert space methods in probability and statistical inference:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1994
|
| Series: | Wiley series in probability and mathematical statistics
A Wiley-Interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 252 S. |
| ISBN: | 0471592811 |
Staff View
MARC
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| 100 | 1 | |a Small, Christopher G. |d 1956- |e Verfasser |0 (DE-588)112053807 |4 aut | |
| 245 | 1 | 0 | |a Hilbert space methods in probability and statistical inference |c Christopher G. Small ; D. L. McLeish |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1994 | |
| 300 | |a XI, 252 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and mathematical statistics | |
| 490 | 0 | |a A Wiley-Interscience publication | |
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| 650 | 7 | |a Statistique mathématique |2 ram | |
| 650 | 4 | |a Statistik | |
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Record in the Search Index
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| adam_text |
Contents
Preface ix
1. Introduction 1
1.1 Objectives of the Book, 1
1.2 The Role of Projection, 5
1.3 Overview of the Book, 7
2. Hilbert Spaces 9
2.1 Vector Spaces, 9
2.2 Hilbert Spaces, 11
2.3 The Hilbert Space L2, 14
2.4 Projection and the Riesz Representation, 19
2.5 Tensor Products, 24
2.6 Notes, 27
Problems, 28
3. Probability Theory 31
3.1 Probability Hilbert Spaces, 31
3.2 Probability Subspaces and Independence, 41
3.3 Conditional Expectation, 46
3.4 Sample Spaces, 49
3.5 Notes, 53
Problems, 54
v
vi CONTENTS
4. Estimating Functions 59
4.1 Unbiased Estimators and Linear Estimating Functions, 59
4.2 Spaces of Estimating Functions, 73
4.3 Local Subspaces, 81
4.4 Projection and E-Rao-Blackwellization, 84
4.5 Roots of Estimating Functions, 87
4.6 Subspaces and Relative E-Sufficiency, 92
4.7 The Standard Product Model, 93
4.8 Correcting for Curvature, 96
4.9 Exponential Families and Quasiexponential Families, 98
4.10 Notes, 102
Problems, 104
5. Orthogonality and Nuisance Parameters 107
5.1 Introduction, 107
5.2 Parameter Orthogonality, 109
5.3 Reducing Sensitivity Using Projection, 110
5.4 Location and Scale Models, 114
5.5 Partial Ancillarity and Partial Sufficiency, 118
5.6 Notes, 121
Problems, 124
6. Martingale Estimating Functions and Projected Likelihood 127
6.1 Introduction, 127
6.2 Discrete Time Martingales and Products, 128
6.3 Martingale Estimating Functions, 132
6.4 Quasilikelihood and Projected Likelihood, 137
6.5 Comparing Quasilikelihood, Product Likelihood,
and Empirical Likelihood, 146
6.6 The Projected Likelihood in the General Case, 149
6.7 An Application to Stable Laws, 151
6.8 Notes, 158
Problems, 158
7. Stochastic Integration and Product Integrals 163
7.1 Continuous Time Martingales, 163
7.2 Predictable Processes, 169
CONTENTS vii
7.3 Introduction to Stochastic Integrals, 170
7.4 The Stochastic Integral and the Linear Isometry, 172
7.5 The Doob-Meyer Decomposition and the Predictable
Variation Process, 176
7.6 Semimartingales, 179
7.7 Product Integrals, 181
7.8 Notes, 183
Problems, 185
8. Estimating Functions and the Product Integral Likelihood
for Continuous Time Stochastic Processes 189
8.1 Introduction, 189
8.2 Continuous Time Martingale Estimating Functions, 194
8.3 A Product Integral Form for the Likelihood, 199
8.4 The Projected Likelihood in the General Case, 203
8.5 Reproducing Kernel Hilbert Spaces, 210
8.6 Linear Estimating Functions, 215
8.7 Notes, 218
Problems, 219
9. Hilbert Spaces and Spline Density Estimation 221
9.1 Histograms and Histofunctions, 221
9.2 Histosplines, 224
9.3 Some Variational Issues, 227
9.4 Bandwidth Selection, 231
9.5 Applications to Stock Market Data, 232
9.6 Notes, 233
Problems, 234
Bibliography 235
Index 245 |
| any_adam_object | 1 |
| author | Small, Christopher G. 1956- McLeish, Don L. 1946- |
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| callnumber-first | Q - Science |
| callnumber-label | QA273 |
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| callnumber-search | QA273.43 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 470 SK 600 SK 800 SK 830 |
| ctrlnum | (OCoLC)844010745 (DE-599)BVBBV023808740 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023808740 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:59:49Z |
| institution | BVB |
| isbn | 0471592811 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017450909 |
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| physical | XI, 252 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and mathematical statistics A Wiley-Interscience publication |
| spelling | Small, Christopher G. 1956- Verfasser (DE-588)112053807 aut Hilbert space methods in probability and statistical inference Christopher G. Small ; D. L. McLeish New York [u.a.] Wiley 1994 XI, 252 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics A Wiley-Interscience publication Hilbert, Espace de Hilbert, espaces de ram Hilbertruimten gtt Probabilités Probabilités ram Statistiek gtt Statistique mathématique Statistique mathématique ram Statistik Hilbert space Mathematical statistics Probabilities Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Hilbert-Raum (DE-588)4159850-7 s Statistik (DE-588)4056995-0 s DE-604 McLeish, Don L. 1946- Verfasser (DE-588)171880978 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017450909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Small, Christopher G. 1956- McLeish, Don L. 1946- Hilbert space methods in probability and statistical inference Hilbert, Espace de Hilbert, espaces de ram Hilbertruimten gtt Probabilités Probabilités ram Statistiek gtt Statistique mathématique Statistique mathématique ram Statistik Hilbert space Mathematical statistics Probabilities Hilbert-Raum (DE-588)4159850-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4079013-7 (DE-588)4056995-0 |
| title | Hilbert space methods in probability and statistical inference |
| title_auth | Hilbert space methods in probability and statistical inference |
| title_exact_search | Hilbert space methods in probability and statistical inference |
| title_full | Hilbert space methods in probability and statistical inference Christopher G. Small ; D. L. McLeish |
| title_fullStr | Hilbert space methods in probability and statistical inference Christopher G. Small ; D. L. McLeish |
| title_full_unstemmed | Hilbert space methods in probability and statistical inference Christopher G. Small ; D. L. McLeish |
| title_short | Hilbert space methods in probability and statistical inference |
| title_sort | hilbert space methods in probability and statistical inference |
| topic | Hilbert, Espace de Hilbert, espaces de ram Hilbertruimten gtt Probabilités Probabilités ram Statistiek gtt Statistique mathématique Statistique mathématique ram Statistik Hilbert space Mathematical statistics Probabilities Hilbert-Raum (DE-588)4159850-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Hilbert, Espace de Hilbert, espaces de Hilbertruimten Probabilités Statistiek Statistique mathématique Statistik Hilbert space Mathematical statistics Probabilities Hilbert-Raum Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017450909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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