Strong approximations in probability and statistics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1981
|
| Schriftenreihe: | Probability and mathematical statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 284 S. |
| ISBN: | 0121985407 |
Internformat
MARC
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| 100 | 1 | |a Csörgő, Miklós |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Strong approximations in probability and statistics |c M. Csörgö and P. Révész |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1981 | |
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| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Probability and mathematical statistics | |
| 650 | 4 | |a Approximation, Théorie de l' | |
| 650 | 4 | |a Probabilités | |
| 650 | 7 | |a Statistiek |2 gtt | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 7 | |a Waarschijnlijkheid (statistiek) |2 gtt | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Invariants | |
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Datensatz im Suchindex
| _version_ | 1823048841829548032 |
|---|---|
| adam_text |
Contents
Preface 9
Introduction 11
1. Wiener and some Related Gaussian Processes 21
1.0 On the notion of a Wiener process 21
1.1 Definition and existence of a Wiener process 21
1.2 How big are the increments of a Wiener process? 29
1.3 The law of iterated logarithm for the Wiener process 36
1.4 Brownian bridges 41
1.5 The distributions of some functionals of the Wiener and Brownian bridge
processes 43
1.6 The modulus of non differentiability of the Wiener process 44
1.7 How small are the increments of a Wiener process? 47
1.8 Infinite series representations of the Wiener process and Brownian bridge 53
1.9 The Ornstein Uhlenbeck process 55
1.10 On the notion of a two parameter Wiener process 57
1.11 Definition and existence of a two parameter Wiener process 58
1.12 How big are the increments of a two parameter Wiener process? 61
1.13 A continuity modulus of W(x, y) 74
1.14 The limit points of W(x, y) as y *°° 75
1.15 The Kiefer process 80
Supplementary remarks 82
2. Strong Approximations of Partial Sums of 1.1. D. R.V. by Wiener Processes. 88
2.0 Notations 88
2.1 A proof of Donsker's theorem with Skorohod's embedding scheme 88
2.2 The strong invariance principle appears 91
2.3 The stochastic Geyser problem as a lower limit to the strong invariance problem 95
2.4 The longest runs of pure heads and the stochastic Geyser problem 97
2.5 Improving the upper limit 101
2.6 The best rates emerge 106
Supplementary remarks 112
6 Contents
3. A Study of Partial Sums with the Hehi of Strong Approximation Methods . 115
3.0 Introduction 115
3.1 How big are the increments of partial sums of I.I.D.R.V. when the moment
generating function exists? 115
3.2 How big are the increments of partial sums of I.I.D.R.V. when the moment
generating function does not exist? 117
3.3 How small are the increments of partial sums of LI. D.R.V.? 120
3.4 A summary 122
Supplementary remarks 122
4. Strong Approximations of Empirical Processes by Gaussian Processes 127
4.1 Some classical results 127
4.2 Why should the empirical process behave like a Brownian bridge? 129
4.3 The first strong approximations of the empirical process 130
4.4 Best strong approximations of the empirical process 133
4.5 Strong approximation of the quantile process 143
Supplementary remarks 154
5. A Study of Empirical and Qnantfle Processes with the Help of Strong Approxi¬
mation Methods 156
5.0 Introduction 156
5.1 The law of iterated logarithm for the empirical process 156
5.2 The distance between the empirical and the quantile processes 160
5.3 The law of iterated logarithm for the quantile process 162
5.4 Asymptotic distribution results for some classical functionals of the empirical
process 163
5.5 Asymptotic distribution results for some classical functionals of the quantile
process 171
5.6 Asymptotic distribution results for some classical functionals of some ifc sample
empirical and quantile processes 181
5.7 Approximations of the empirical process when parameters are estimated 188
5.8 Asymptotic quadratic quantile tests for composite goodness of fit 202
5.9 On testing for exponentiality 213
Supplementary remarks 216
6. A Study of Furtbw Empirical Processes with the Help of Strong Approxlmatloa
Methods 219
6.0 Introduction 219
6.1 Strong invariance principles and limit distributions for empirical densities 219
6.2 Strong theorems for empirical densities 230
6.3 Empirical regression 237
Contents 7
6.4 Empirical characteristic functions 242
Supplementary remarks 248
7. Random Limit Theorems via Strong Invariance Principles 250
7.0 Introduction and some historical remarks 250
7.1 Laws of large numbers for randomly selected sequences 252
7.2 Invariance (strong and weak) principles for random sum limit theorems 255
7.3 Invariance (strong and weak) principles for random size empirical processes 261
References 263
Author Index 277
Subject Index 281
Summary of Notations and Abbreviations 283 |
| any_adam_object | 1 |
| author | Csörgő, Miklós Révész, Pál |
| author_facet | Csörgő, Miklós Révész, Pál |
| author_role | aut aut |
| author_sort | Csörgő, Miklós |
| author_variant | m c mc p r pr |
| building | Verbundindex |
| bvnumber | BV001998684 |
| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)633528961 (DE-599)BVBBV001998684 |
| 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 Wirtschaftswissenschaften |
| format | Book |
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| genre | Stochastischer gnd |
| genre_facet | Stochastischer |
| id | DE-604.BV001998684 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T15:00:57Z |
| institution | BVB |
| isbn | 0121985407 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001303759 |
| oclc_num | 633528961 |
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| physical | 284 S. |
| psigel | TUB-nvmb |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Acad. Press |
| record_format | marc |
| series2 | Probability and mathematical statistics |
| spelling | Csörgő, Miklós Verfasser aut Strong approximations in probability and statistics M. Csörgö and P. Révész New York [u.a.] Acad. Press 1981 284 S. txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics Approximation, Théorie de l' Probabilités Statistiek gtt Statistique mathématique Waarschijnlijkheid (statistiek) gtt Statistik Approximation theory Invariants Prozess (DE-588)4047577-3 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Stochastische Approximation (DE-588)4183371-5 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer gnd rswk-swf Stochastische Approximation (DE-588)4183371-5 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Approximationstheorie (DE-588)4120913-8 s Stochastischer f Prozess (DE-588)4047577-3 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Révész, Pál Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Csörgő, Miklós Révész, Pál Strong approximations in probability and statistics Approximation, Théorie de l' Probabilités Statistiek gtt Statistique mathématique Waarschijnlijkheid (statistiek) gtt Statistik Approximation theory Invariants Prozess (DE-588)4047577-3 gnd Approximationstheorie (DE-588)4120913-8 gnd Stochastische Approximation (DE-588)4183371-5 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4047577-3 (DE-588)4120913-8 (DE-588)4183371-5 (DE-588)4079013-7 (DE-588)4057630-9 |
| title | Strong approximations in probability and statistics |
| title_auth | Strong approximations in probability and statistics |
| title_exact_search | Strong approximations in probability and statistics |
| title_full | Strong approximations in probability and statistics M. Csörgö and P. Révész |
| title_fullStr | Strong approximations in probability and statistics M. Csörgö and P. Révész |
| title_full_unstemmed | Strong approximations in probability and statistics M. Csörgö and P. Révész |
| title_short | Strong approximations in probability and statistics |
| title_sort | strong approximations in probability and statistics |
| topic | Approximation, Théorie de l' Probabilités Statistiek gtt Statistique mathématique Waarschijnlijkheid (statistiek) gtt Statistik Approximation theory Invariants Prozess (DE-588)4047577-3 gnd Approximationstheorie (DE-588)4120913-8 gnd Stochastische Approximation (DE-588)4183371-5 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Approximation, Théorie de l' Probabilités Statistiek Statistique mathématique Waarschijnlijkheid (statistiek) Statistik Approximation theory Invariants Prozess Approximationstheorie Stochastische Approximation Wahrscheinlichkeitstheorie Stochastischer Prozess Stochastischer |
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