Verfügbarkeit: Theory of U-statistics | Technische Universität München

Theory of U-statistics:

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Bibliographische Detailangaben
Beteiligte Personen:	Koroljuk, Volodymyr S. 1925- (VerfasserIn), Borovskich, Jurij V. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Dordrecht u.a. Kluwer Acad. Publ. 1994
Schriftenreihe:	Mathematics and its applications 273
Schlagwörter:	U-statistics Statistik U-Statistik U-Stichprobenfunktion Grenzwertsatz
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006512041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	IX, 552 S.
ISBN:	0792326083

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS Preface ix Introduction 1 CHAPTER 1. BASIC DEFINITIONS AND NOTIONS 17 1.1. One sample [/ statistics 17 1.2. Multi sample {/ statistics 35 1.3. Von Mises functionals 39 1.4. Functions of (/ statistics 42 1.5. Symmetric statistics 46 1.6. Differentiable statistical functions 48 1.7. Permanents and (/ statistics 54 1.8. Multiple stochastic integrals 65 CHAPTER 2. GENERAL INEQUALITIES 69 2.1. Moment inequalities 69 2.2. Maximal inequalities 76 2.3. Estimates of characteristic functions 83 CHAPTER 3. THE LAW OF LARGE NUMBERS 93 3.1. The strong law of large numbers for one sample (/ statistics 93 3.2. The strong law of large numbers for multi sample (/ statistics 96 3.3. Laws of large numbers for functions of (/ statistics 102 3.4. Estimates of the rate of convergence in the laws of large numbers 107 CHAPTER 4. WEAK CONVERGENCE 119 4.1. Asymptotics of random permanents 119 4.2. The Central limit theorem 128 4.3. Orthogonal expansions and (/ statistics 137 4.4. Asymptotic distributions of (/ statistics of arbitrary degree 143 4.5. Multi sample (/ statistics 151 4.6. Limiting distributions of symmetric statistics 159 4.7. (/ statistical scheme of series 160 v vi Contents 4.8. Incomplete (/ statistics 179 4.9. Generalized (/ statistics and random symmetric polynomials 185 4.10. Asymptotics of (/// statistics 191 4.11. (/5 statistics 211 CHAPTER 5. FUNCTIONAL LIMIT THEOREMS 221 5.1. Weak convergence of probability measures in functional spaces 221 5.2. Invariance principle in non degenerate case 223 5.3. Weak convergence of processes in degenerate case 233 5.4. Invariance principle for (/ statistics with antisymmetric kernel 241 5.5. Invariance principle for symmetric statistics 245 5.6. Multi sample invariance principle under condition of degeneracy 252 5.7. Functional limit theorems for [/ statistics with varying kernel 258 CHAPTER 6. APPROXIMATION IN LIMIT THEOREMS 265 6.1. General methods of analysis 265 6.2. Estimations in the central limit theorem 269 6.3. Estimates for multi sample (/ statistics 304 6.4. Functions of (/ statistics 317 6.5. Symmetric statistics 323 6.6. Method of orthogonal expansions in estimation of the rate of convergence 333 6.7. (/// statistics 352 6.8. Estimates in the central limit theorem in infinite dimensional spaces 362 CHAPTER 7. ASYMPTOTIC EXPANSIONS 381 7.1. General form of expansions 381 7.2. Expansions in central limit theorem 382 7.3. Expansions with degenerate kernel 399 7.4. General method of deriving asymptotic expansions 401 7.5. Expansions for linear combination of degenerate von Mises functionals 410 7.6. Expansions for von Mises functionals with kernel of arbitrary order of degeneracy 418 7.7. Moment expansions 422 CHAPTER 8. PROBABILITIES OF LARGE DEVIATIONS 429 8.1. Exponential inequalities 429 8.2. Moderate deviations 431 8.3. Power zones of normal convergence 433 8.4. Large deviations for studentized (/ statistics 435 Contents vii CHAPTER 9. THE LAW OF ITERATED LOGARITHM 443 9.1. The classical law of iterated logarithm with nondegenerate kernel 443 9.2. Strong approximation of [//{ statistics 444 9.3. The functional law of iterated logarithm 451 9.4. The law of iterated logarithm for {/// statistics 455 CHAPTER 10. DEPENDENT VARIABLES 461 10.1. Exchangeable random variables and rank statistics 461 10.2. Weakly exchangeable random variables 471 10.3. Samplings of finite populations 481 10.4. Weakly dependent random variables 483 10.5. Bootstrap variables 495 10.6. Ordinal statistics 501 Historical and bibliographical notes 503 References 515 Subject Index 551
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indexdate	2024-12-20T09:43:02Z
institution	BVB
isbn	0792326083
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-006512041
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physical	IX, 552 S.
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publisher	Kluwer Acad. Publ.
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series	Mathematics and its applications
series2	Mathematics and its applications
spellingShingle	Koroljuk, Volodymyr S. 1925- Borovskich, Jurij V. Theory of U-statistics Mathematics and its applications U-statistics Statistik (DE-588)4056995-0 gnd U-Statistik (DE-588)4754777-7 gnd U-Stichprobenfunktion (DE-588)4279548-5 gnd Grenzwertsatz (DE-588)4158163-5 gnd
subject_GND	(DE-588)4056995-0 (DE-588)4754777-7 (DE-588)4279548-5 (DE-588)4158163-5
title	Theory of U-statistics
title_alt	Teorija U-statistik
title_auth	Theory of U-statistics
title_exact_search	Theory of U-statistics
title_full	Theory of U-statistics by V. S. Koroljuk and Yu. V. Borovskich
title_fullStr	Theory of U-statistics by V. S. Koroljuk and Yu. V. Borovskich
title_full_unstemmed	Theory of U-statistics by V. S. Koroljuk and Yu. V. Borovskich
title_short	Theory of U-statistics
title_sort	theory of u statistics
topic	U-statistics Statistik (DE-588)4056995-0 gnd U-Statistik (DE-588)4754777-7 gnd U-Stichprobenfunktion (DE-588)4279548-5 gnd Grenzwertsatz (DE-588)4158163-5 gnd
topic_facet	U-statistics Statistik U-Statistik U-Stichprobenfunktion Grenzwertsatz
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006512041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV008163334
work_keys_str_mv	AT koroljukvolodymyrs teorijaustatistik AT borovskichjurijv teorijaustatistik AT koroljukvolodymyrs theoryofustatistics AT borovskichjurijv theoryofustatistics

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