Uniform central limit theorems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Cambridge Univ. Press
2014
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| Edition: | 2. ed. |
| Series: | Cambridge studies in advanced mathematics
142 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 472 S. |
| ISBN: | 9780521498845 9780521738415 |
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Record in the Search Index
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| adam_text | Titel: Uniform central limit theorems
Autor: Dudley, Richard M
Jahr: 2014
Contents Preface to the Second Edition page xi 1 Donsker’s Theorem and Inequalities 1 1.1 Empirical Processes: The Classical Case 6 1.2 Metric Entropy and Capacity 7 1.3 Inequalities 9 1.4 *Proof of the Bretagnolle-Massart Theorem 15 1.5 The DKW Inequality in Massart’s Form 39 2 Gaussian Processes; Sample Continuity 61 2.1 General Empirical and Gaussian Processes 61 2.2 Some Definitions 62 2.3 Bounds for Gaussian Vectors 67 2.4 Inequalities for Gaussian Distributions 73 2.5 Sample Boundedness 82 2.6 Gaussian Measures and Convexity 85 2.7 Regularity of the Isonormal Process 88 2.B A Metric Entropy Condition for Continuity 94 2.9 Gaussian Concentration Inequalities 100 2.10 Generic Chaining 108 2.11 Homogeneous and Quasi-Homogeneous Sets in H 117 2.12 Sample Continuity and Compactness 121 2.13 Two-Series and One-Series Theorems 125 3 Definition of Donsker Classes 133 3.1 Definitions: Convergence in Law 133 3.2 Measurable Cover Functions 137 3.3 Almost Uniform, Outer Probability Convergence 143 Vil
Contents viii 3.4 Perfect Functions 145 3.5 Almost Surely Convergent Realizations 149 3.6 Conditions Equivalent to Convergence in Law 154 3.7 Asymptotic Equicontinuity 159 3.8 Unions of Donsker Classes 162 3.9 Sequences of Sets and Functions 163 3.10 Donsker Classes and Sequential Limits 168 3.11 Convex Hulls of Donsker Classes 168 4 Vapnik-Cervonenkis Combinatorics 175 4.1 Vapnik-Cervonenkis Classes of Sets 175 4.2 Generating Vapnik-Cervonenkis Classes 179 4.3 ^Maximal Classes 183 4.4 *Classes of Index 1 185 4.5 *Combining VC Classes 192 4.6 Probability Laws and Independence 200 4.7 VC Properties of Function Classes 204 4.8 Classes of Functions and Dual Density 205 5 Measurability 213 5.1 Sufficiency 215 5.2 Admissibility 222 5.3 Suslin Properties and Selection 229 6 Limit Theorems for VC-Type Classes 239 6.1 Glivenko-Cantelli Theorems 239 6.2 Glivenko-Cantelli Properties for Given P 247 6.3 Pollard’s Central Limit Theorem 251 6.4 Necessary Conditions for Limit Theorems 260 7 Metric Entropy with Bracketing 269 7.1 The Blum-DeHardt Theorem 269 7.2 Bracketing Central Limit Theorems 274 7.3 The Power Set of a Countable Set 279 8 Approximation of Functions and Sets 284 8.1 Introduction: The Hausdorff Metric 284 8.2 Spaces of Differentiable Functions and Sets 287 8.3 Lower Layers 300 8.4 Metric Entropy of Classes of Convex Sets 305 9 Two Samples and the Bootstrap 319 9.1 The Two-Sample Case 319
Contents ix 9.2 A Bootstrap CLT 323 9.3 Other Aspects of the Bootstrap 345 10 Uniform and Universal Limit Theorems 348 10.1 Uniform Glivenko-Cantelli Classes 348 10.2 Universal Donsker Classes 360 10.3 Metric Entropy of Convex Hulls in Hilbert Space 366 10.4 Uniform Donsker Classes 372 10.5 Universal Glivenko-Cantelli Classes 388 11 Classes Too Large to Be Donsker 391 11.1 Universal Lower Bounds 391 11.2 An Upper Bound 393 11.3 Poissonization and Random Sets 395 11.4 Lower Bounds in Borderline Cases 400 11.5 Proof of Theorem 11.10 410 Appendices A Differentiating under an Integral Sign 417 B Multinomial Distributions 424 C Measures on Nonseparable Metric Spaces 427 D An Extension of Lusin’s Theorem 430 E Bochner and Pettis Integrals 432 F Nonexistence of Some Linear Forms 437 G Separation of Analytic Sets 440 H Young-Orlicz Spaces 443 I Versions of Isonormal Processes 446 Bibliography 449 Notation Index 463 Author Index 465 Subject Index 468
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| dewey-tens | 510 - Mathematics |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:08:19Z |
| institution | BVB |
| isbn | 9780521498845 9780521738415 |
| language | English |
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| physical | XII, 472 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Dudley, Richard M. 1938- Verfasser (DE-588)121010996 aut Uniform central limit theorems R. M. Dudley 2. ed. New York, NY Cambridge Univ. Press 2014 XII, 472 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 142 Zentraler Grenzwertsatz Central limit theorem Zentraler Grenzwertsatz (DE-588)4067618-3 gnd rswk-swf Zentraler Grenzwertsatz (DE-588)4067618-3 s DE-604 Cambridge studies in advanced mathematics 142 (DE-604)BV000003678 142 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027363072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dudley, Richard M. 1938- Uniform central limit theorems Cambridge studies in advanced mathematics Zentraler Grenzwertsatz Central limit theorem Zentraler Grenzwertsatz (DE-588)4067618-3 gnd |
| subject_GND | (DE-588)4067618-3 |
| title | Uniform central limit theorems |
| title_auth | Uniform central limit theorems |
| title_exact_search | Uniform central limit theorems |
| title_full | Uniform central limit theorems R. M. Dudley |
| title_fullStr | Uniform central limit theorems R. M. Dudley |
| title_full_unstemmed | Uniform central limit theorems R. M. Dudley |
| title_short | Uniform central limit theorems |
| title_sort | uniform central limit theorems |
| topic | Zentraler Grenzwertsatz Central limit theorem Zentraler Grenzwertsatz (DE-588)4067618-3 gnd |
| topic_facet | Zentraler Grenzwertsatz Central limit theorem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027363072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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