U-statistics in Banach spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht
VSP
1996
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 420 S. |
| ISBN: | 9067642002 |
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MARC
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| 100 | 1 | |a Borovskich, Jurij V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a U-statistics in Banach spaces |c Yu. V. Borovskikh |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht |b VSP |c 1996 | |
| 300 | |a XII, 420 S. | ||
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Record in the Search Index
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| adam_text | Contents
Preface xi
Introduction 1
1 Basic definitions 5
1.1 One sample (7B statistics 5
1.2 Multi sample l/B statistics 15
1.3 Von Mises statistics 21
1.4 Banach valued symmetric statistics 23
1.5 Permanent symmetric statistics 24
1.6 Multiple stochastic integrals 27
1.7 B valued polynomial chaos 29
2 Inequalities 31
2.1 Inequalities based on the Hoeffding formula 31
2.2 Martingale moment inequalities 37
2.3 Maximal inequalities 42
2.4 Contraction and symmetrization inequalities 44
2.5 Decoupling inequalities 48
2.6 Hypercontractive method in moment inequalities 64
2.7 Moment inequalities in Banach spaces of type p 71
3 Law of large numbers 73
3.1 One sample (/B statistics 73
3.2 Multi sample f/B statistics 79
3.3 Von Mises statistics 84
3.4 Estimates of convergence rates 86
4 Weak convergence 95
4.1 Central limit theorem 95
4.2 Convergence to a chaos 102
4.3 Multi sample f7B statistics 114
vii
viii Contents
4.4 Poisson approximation 124
4.5 Stable approximation 129
4.6 Approximation with increasing degrees 132
4.7 Symmetric statistics 146
4.8 [/ statistics with varying kernels 152
4.9 Weighted [/ statistics 160
5 Functional limit theorems 165
5.1 Non degenerate kernels 166
5.2 Degenerate kernels 170
5.3 Weak convergence to a chaos process 174
5.4 Weak convergence in the Poisson approximation scheme 182
5.5 Invariance principle for symmetric statistics 184
5.6 Functional limit theorems with varying kernels 187
5.7 Weak convergence of [/ processes 191
6 Approximation estimates 201
6.1 General methods of estimation 201
6.2 Rate of normal approximation of l/R statistics 205
6.3 Estimates with increasing degree 215
6.4 Nonuniform estimates 224
6.5 Rate of chaos approximation 226
6.6 Normal approximation of [/H statistics 237
6.7 Multi sample UH statistics 277
6.8 Estimates in central limit theorem in ^p 279
6.9 Rate of Poisson approximation 291
7 Asymptotic expansions 295
7.1 Expansions for non degenerate f/ii statistics 296
7.2 General method of expansions 311
7.3 Expansions with canonical kernels 316
7.4 Expansions with arbitrary kernels 323
8 Large deviations 327
8.1 Exponential inequalities 327
8.2 Moderate deviations 335
8.3 Power zones of normal convergence 337
8.4 Probabilities of large deviations for t/H statistics 339
Contents ix
9 Law of iterated logarithm 349
9.1 [/R statistics 350
9.2 l/H statistics 351
9.3 Bounded LIL 352
9.4 Compact LIL 357
9.5 Functional LIL 360
9.6 Multi sample [/B statistics 361
10 Dependent variables 365
10.1 Symmetrically dependent random variables 365
10.2 Weakly dependent random variables 366
10.3 Bootstrap variables 369
10.4 Order statistics 375
Bibliographical supplements and comments 377
Bibliography 385
Index 419
|
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| author_facet | Borovskich, Jurij V. |
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| id | DE-604.BV011175591 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:15Z |
| institution | BVB |
| isbn | 9067642002 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007493320 |
| oclc_num | 247611700 |
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| owner_facet | DE-12 DE-824 DE-19 DE-BY-UBM DE-11 |
| physical | XII, 420 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | VSP |
| record_format | marc |
| spelling | Borovskich, Jurij V. Verfasser aut U-statistics in Banach spaces Yu. V. Borovskikh 1. publ. Utrecht VSP 1996 XII, 420 S. txt rdacontent n rdamedia nc rdacarrier Banach-Raum (DE-588)4004402-6 gnd rswk-swf U-Stichprobenfunktion (DE-588)4279548-5 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s DE-604 U-Stichprobenfunktion (DE-588)4279548-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007493320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borovskich, Jurij V. U-statistics in Banach spaces Banach-Raum (DE-588)4004402-6 gnd U-Stichprobenfunktion (DE-588)4279548-5 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4279548-5 |
| title | U-statistics in Banach spaces |
| title_auth | U-statistics in Banach spaces |
| title_exact_search | U-statistics in Banach spaces |
| title_full | U-statistics in Banach spaces Yu. V. Borovskikh |
| title_fullStr | U-statistics in Banach spaces Yu. V. Borovskikh |
| title_full_unstemmed | U-statistics in Banach spaces Yu. V. Borovskikh |
| title_short | U-statistics in Banach spaces |
| title_sort | u statistics in banach spaces |
| topic | Banach-Raum (DE-588)4004402-6 gnd U-Stichprobenfunktion (DE-588)4279548-5 gnd |
| topic_facet | Banach-Raum U-Stichprobenfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007493320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT borovskichjurijv ustatisticsinbanachspaces |