Limit theory for mixing dependent random variables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Science Press [u.a.]
1996
|
| Series: | Mathematics and its applications
378 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 426 S. |
| ISBN: | 0792342194 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface vii
Part I Introduction 1
Chapter 1 Definitions and Basic Inequalities 3
1.1 Definitions 3
1.2 Basic inequalities 7
Chapter 2 Moment Estimations of Partial Sums 15
2.1 Variances of partial sums • . 15
2.2 Further inequalitis 24
Part II Weak Convergence 39
Chapter 3 Weak Convergence for a mixing Sequences 41
3.1 Necessary and sufficient conditions for the CLT 41
3.2 Sufficient conditions for CLT and WIP 51
3.3 The CLT and WIP when the variance is infinite 63
Chapter 4 Weak Convergence for p mixing Sequences 71
4.1 The WIP when the moments of order 2 are finite 73
4.2 The WIP when moments of higher than two orders 78
4.3 A generalized result when moments of
higher than two orders 88
4.4 The WIP when the variance is infinite 104
Chapter 5 Weak Convergence for p mixing Sequences 123
5.1 The WIP when the moments of order 2 are finite 124
5.2 The Ibragimov Linnik Iosifescu conjecture 136
Chapter 6 Weak Convergence for Mixing Random Fields 141
6.1 The CLT for mixing random fields 141
6.2 Convergence of finite dimensional distributions 149
6.3 Tightness 160
X Contents
Chapter 7 The Berry Esseen Inequality and the Rate
of Weak Convergence 169
7.1 Rate of convergence in distribution for a mixing
and p mixing sequences 169
7.2 The rate of weak convergence for a ^ mixing sequence 181
Part III Almost Sure Convergence and
Strong Approximations 189
Chapter 8 Laws of Large Numbers and Complete Convergence 191
• 8.1 Weak law of large numbers 191
8.2 Strong laws of large numbers 199
8.3 Complete convergence for (^ mixing sequences 201
8.4 Complete convergence for /o mixing sequences 208
8.5 Complete convergence for a mixing sequences 222
8.6 A further discussion on the complete convergence 231
Chapter 9 Strong Approximations 241
9.1 Strong approximations for a (^ mixing sequence 241
9.2 Strong approximations for a p mixing sequence 247
9.3 Strong approximations for a a mixing sequence 263
Chapter 10 The Increments of Partial Sums 269
10.1 Some lemmas 269
10.2 How big are the increments when the moment
generation functions exist? 277
10.3 How big are the increments when the moment
generating functions do not exist? 283
Chapter 11 Strong Approximations for Mixing Random Fields 287
11.1 Strong approximations of a y mixing random field 288
11.2 Strong approximations of a a mixing random fields 301
Part IV Statistics of a Dependent Sample 309
Chapter 12 Empirical Processes : 311
12.1 Weak convergence 312
12.2 Weighted weak convergence 317
12.3 Strong approximations 331
12.4 Moduli of continuity of empirical processes 341
Contents xi
Chapter 13 Convergence of Some Statistics with
a Mixing Sample 347
13.1 U Statistics 347
13.2 Error variance estimations in linear models 360
13.3 Density estimations 369
Chapter 14 Strong Approximations for Other Kinds of
Dependent Random Variables 379
14.1 Lacunary trigonometric series with weights 379
14.2 A class of Gaussian sequences 392
14.3 The non negative additive functional of a Markov process ... 397
Appendix 406
References 409
Index . ¦. i.: 425
|
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| dewey-raw | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011570342 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:00Z |
| institution | BVB |
| isbn | 0792342194 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007790310 |
| oclc_num | 35172675 |
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| owner | DE-384 DE-824 DE-739 DE-703 |
| owner_facet | DE-384 DE-824 DE-739 DE-703 |
| physical | XI, 426 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Science Press [u.a.] |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Lin, Zhengyan Verfasser aut Limit theory for mixing dependent random variables Lin Zhengyan and Lu Chuanrong New York [u.a.] Science Press [u.a.] 1996 XI, 426 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 378 Limiettheorema's gtt Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Stochastische Abhängigkeit (DE-588)4220425-2 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Zufallsvariable (DE-588)4129514-6 s Stochastische Abhängigkeit (DE-588)4220425-2 s Grenzwertsatz (DE-588)4158163-5 s Lu, Chuanrong Verfasser aut Mathematics and its applications 378 (DE-604)BV008163334 378 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007790310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, Zhengyan Lu, Chuanrong Limit theory for mixing dependent random variables Mathematics and its applications Limiettheorema's gtt Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Stochastische Abhängigkeit (DE-588)4220425-2 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Zufallsvariable (DE-588)4129514-6 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4220425-2 (DE-588)4079013-7 (DE-588)4129514-6 (DE-588)4158163-5 |
| title | Limit theory for mixing dependent random variables |
| title_auth | Limit theory for mixing dependent random variables |
| title_exact_search | Limit theory for mixing dependent random variables |
| title_full | Limit theory for mixing dependent random variables Lin Zhengyan and Lu Chuanrong |
| title_fullStr | Limit theory for mixing dependent random variables Lin Zhengyan and Lu Chuanrong |
| title_full_unstemmed | Limit theory for mixing dependent random variables Lin Zhengyan and Lu Chuanrong |
| title_short | Limit theory for mixing dependent random variables |
| title_sort | limit theory for mixing dependent random variables |
| topic | Limiettheorema's gtt Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Stochastische Abhängigkeit (DE-588)4220425-2 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Zufallsvariable (DE-588)4129514-6 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Limiettheorema's Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Stochastische Abhängigkeit Wahrscheinlichkeitstheorie Zufallsvariable Grenzwertsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007790310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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