Approximation theorems of mathematical statistics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u. a.]
Wiley
2002
|
| Ausgabe: | paperback ed. |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 371 S. |
| ISBN: | 0471219274 9780471219279 |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Approximation theorems of mathematical statistics
Autor: Serfling, Robert J.
Jahr: 2002
Contents
1 Preliminary Tools and Foundations 1
1.1 Preliminary Notation and Definitions, 1
1.2 Modes of Convergence of a Sequence
of Random Variables, 6
1.3 Relationships Among the Modes of Convergence, 9
1.4 Convergence of Moments ; Uniform Integrability, 13
1.5 Further Discussion of Convergence
in Distribution, 16
1.6 Operations on Sequences to Produce
Specified Convergence Properties, 22
1.7 Convergence Properties of Transformed Sequences, 24
1.8 Basic Probability Limit Theorems :
The WLLN and SLLN, 26
1.9 Basic Probability Limit Theorems : The CLT, 28
1.10 Basic Probability Limit Theorems: The LIL, 35
1.11 Stochastic Process Formulation of the CLT, 37
1.12 Taylor s Theorem ; Differentials, 43
1.13 Conditions for Determination of a
Distribution by Its Moments, 45
1.14 Conditions for Existence of Moments
of a Distribution, 46
1.15 Asymptotic Aspects of Statistical
Inference Procedures, 47
l.P Problems, 52
2 The Bask Sample Statistics
2.1 The Sample Distribution Function, 56
2.2 The Sample Moments, 66
2.3 The Sample Quantités, 74
2.4 The Order Statistics, 87
xi
XU CONTENTS
2.5 Asymptotic Representation Theory for Sample
Quantités, Order Statistics, and Sample
Distribution Functions, 91
2.6 Confidence Intervals for Quantiles, 102
2.7 Asymptotic Multivariate Normality of Cell
Frequency Vectors, 107
2.8 Stochastic Processes Associated with a Sample, 109
2.P Problems, 113
3 Transformations of Given Statistics 117
3.1 Functions of Asymptotically Normal Statistics :
Uni variate Case, 118
3.2 Examples and Applications, 120
3.3 Functions of Asymptotically Normal Vectors, 122
3.4 Further Examples and Applications, 125
3.5 Quadratic Forms in Asymptotically Multivariate
Normal Vectors, 128
3.6 Functions of Order Statistics, 134
3.P Problems, 136
4 Asymptotic Theory in Parametric Inference 138
4.1 Asymptotic Optimally in Estimation, 138
4.2 Estimation by the Method of Maximum Likelihood, 143
4.3 Other Approaches toward Estimation, 150
4.4 Hypothesis Testing by Likelihood Methods, 151
4.5 Estimation via Product-Multinomial Data, 160
4.6 Hypothesis Testing via Product-Multinomial Data, 165
4.P Problems, 169
5 U-Statistics 171
5.1 Basic Description of {/-Statistics, 172
5.2 The Variance and Other Moments of a ¿/-Statistic, 181
5.3 The Projection of a {/-Statistic on the
Basic Observations, 187
5.4 Almost Sure Behavior of {/-Statistics, 190
5.5 Asymptotic Distribution Theory of {/-Statistics, 192
5.6 Probability Inequalities and Deviation
Probabilities for U-Statistics, 199
5.7 Complements, 203
5.P Problems, 207
CONTENTS xiii
6 Von Mises Differentiate Statistical Fractions 210
6.1 Statistics Considered as Functions of the Sample
Distribution Function, 211
6.2 Reduction to a Differential Approximation, 214
6.3 Methodology for Analysis of the Differential
Approximation, 221
6.4 Asymptotic Properties of Differentiable
Statistical Functions, 225
6.5 Examples, 231
6.6 Complements, 238
6.P Problems, 241
7 M-Estimates 243
7.1 Basic Formulation and Examples, 243
7.2 Asymptotic Properties of Af-Estimates, 248
7.3 Complements, 257
7.P Problems, 260
8 L-Estimates 262
8.1 Basic Formulation and Examples, 262
8.2 Asymptotic Properties of L-Estimates, 271
8.P Problems, 290
9 R-Estimates 292
9.1 Basic Formulation and Examples, 292
9.2 Asymptotic Normality of Simple Linear Rank
Statistics, 295
9.3 Complements, 311
9.P Problems, 312
10 Asymptotic Relative Efficiency 314
10.1 Approaches toward Comparison of
Test Procedures, 314
10.2 The Pitman Approach, 316
10.3 The Chernoff Index, 325
10.4 Bahadur s Stochastic Comparison, 332
10.5 The Hodges-Lehmann Asymptotic Relative
Efficiency, 341
Xhr CONTENTS
10.6 Hocffding s Investigation (Multinomial
Distributions), 342
10.7 The Rubin-Sethuraman Bayes Risk Efficiency, 347
10.P Problems, 348
Appendix 351
References 353
Author Index 365
Subject Index 369
|
| adam_txt |
Titel: Approximation theorems of mathematical statistics
Autor: Serfling, Robert J.
Jahr: 2002
Contents
1 Preliminary Tools and Foundations 1
1.1 Preliminary Notation and Definitions, 1
1.2 Modes of Convergence of a Sequence
of Random Variables, 6
1.3 Relationships Among the Modes of Convergence, 9
1.4 Convergence of Moments ; Uniform Integrability, 13
1.5 Further Discussion of Convergence
in Distribution, 16
1.6 Operations on Sequences to Produce
Specified Convergence Properties, 22
1.7 Convergence Properties of Transformed Sequences, 24
1.8 Basic Probability Limit Theorems :
The WLLN and SLLN, 26
1.9 Basic Probability Limit Theorems : The CLT, 28
1.10 Basic Probability Limit Theorems: The LIL, 35
1.11 Stochastic Process Formulation of the CLT, 37
1.12 Taylor's Theorem ; Differentials, 43
1.13 Conditions for Determination of a
Distribution by Its Moments, 45
1.14 Conditions for Existence of Moments
of a Distribution, 46
1.15 Asymptotic Aspects of Statistical
Inference Procedures, 47
l.P Problems, 52
2 The Bask Sample Statistics
2.1 The Sample Distribution Function, 56
2.2 The Sample Moments, 66
2.3 The Sample Quantités, 74
2.4 The Order Statistics, 87
xi
XU CONTENTS
2.5 Asymptotic Representation Theory for Sample
Quantités, Order Statistics, and Sample
Distribution Functions, 91
2.6 Confidence Intervals for Quantiles, 102
2.7 Asymptotic Multivariate Normality of Cell
Frequency Vectors, 107
2.8 Stochastic Processes Associated with a Sample, 109
2.P Problems, 113
3 Transformations of Given Statistics 117
3.1 Functions of Asymptotically Normal Statistics :
Uni variate Case, 118
3.2 Examples and Applications, 120
3.3 Functions of Asymptotically Normal Vectors, 122
3.4 Further Examples and Applications, 125
3.5 Quadratic Forms in Asymptotically Multivariate
Normal Vectors, 128
3.6 Functions of Order Statistics, 134
3.P Problems, 136
4 Asymptotic Theory in Parametric Inference 138
4.1 Asymptotic Optimally in Estimation, 138
4.2 Estimation by the Method of Maximum Likelihood, 143
4.3 Other Approaches toward Estimation, 150
4.4 Hypothesis Testing by Likelihood Methods, 151
4.5 Estimation via Product-Multinomial Data, 160
4.6 Hypothesis Testing via Product-Multinomial Data, 165
4.P Problems, 169
5 U-Statistics 171
5.1 Basic Description of {/-Statistics, 172
5.2 The Variance and Other Moments of a ¿/-Statistic, 181
5.3 The Projection of a {/-Statistic on the
Basic Observations, 187
5.4 Almost Sure Behavior of {/-Statistics, 190
5.5 Asymptotic Distribution Theory of {/-Statistics, 192
5.6 Probability Inequalities and Deviation
Probabilities for U-Statistics, 199
5.7 Complements, 203
5.P Problems, 207
CONTENTS xiii
6 Von Mises Differentiate Statistical Fractions 210
6.1 Statistics Considered as Functions of the Sample
Distribution Function, 211
6.2 Reduction to a Differential Approximation, 214
6.3 Methodology for Analysis of the Differential
Approximation, 221
6.4 Asymptotic Properties of Differentiable
Statistical Functions, 225
6.5 Examples, 231
6.6 Complements, 238
6.P Problems, 241
7 M-Estimates 243
7.1 Basic Formulation and Examples, 243
7.2 Asymptotic Properties of Af-Estimates, 248
7.3 Complements, 257
7.P Problems, 260
8 L-Estimates 262
8.1 Basic Formulation and Examples, 262
8.2 Asymptotic Properties of L-Estimates, 271
8.P Problems, 290
9 R-Estimates 292
9.1 Basic Formulation and Examples, 292
9.2 Asymptotic Normality of Simple Linear Rank
Statistics, 295
9.3 Complements, 311
9.P Problems, 312
10 Asymptotic Relative Efficiency 314
10.1 Approaches toward Comparison of
Test Procedures, 314
10.2 The Pitman Approach, 316
10.3 The Chernoff Index, 325
10.4 Bahadur's "Stochastic Comparison," 332
10.5 The Hodges-Lehmann Asymptotic Relative
Efficiency, 341
Xhr CONTENTS
10.6 Hocffding's Investigation (Multinomial
Distributions), 342
10.7 The Rubin-Sethuraman " Bayes Risk " Efficiency, 347
10.P Problems, 348
Appendix 351
References 353
Author Index 365
Subject Index 369 |
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| index_date | 2024-07-02T22:28:42Z |
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| spelling | Serfling, Robert J. Verfasser (DE-588)1068473967 aut Approximation theorems of mathematical statistics Robert J. Serfling paperback ed. New York, NY [u. a.] Wiley 2002 XIV, 371 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Teoremas limites larpcal Teoria assintótica (inferência estatística) larpcal Limit theorems (Probability theory) Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Approximation (DE-588)4002498-2 s Statistik (DE-588)4056995-0 s DE-604 Grenzwertsatz (DE-588)4158163-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016813010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Serfling, Robert J. Approximation theorems of mathematical statistics Teoremas limites larpcal Teoria assintótica (inferência estatística) larpcal Limit theorems (Probability theory) Mathematical statistics Statistik (DE-588)4056995-0 gnd Grenzwertsatz (DE-588)4158163-5 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4158163-5 (DE-588)4002498-2 |
| title | Approximation theorems of mathematical statistics |
| title_auth | Approximation theorems of mathematical statistics |
| title_exact_search | Approximation theorems of mathematical statistics |
| title_exact_search_txtP | Approximation theorems of mathematical statistics |
| title_full | Approximation theorems of mathematical statistics Robert J. Serfling |
| title_fullStr | Approximation theorems of mathematical statistics Robert J. Serfling |
| title_full_unstemmed | Approximation theorems of mathematical statistics Robert J. Serfling |
| title_short | Approximation theorems of mathematical statistics |
| title_sort | approximation theorems of mathematical statistics |
| topic | Teoremas limites larpcal Teoria assintótica (inferência estatística) larpcal Limit theorems (Probability theory) Mathematical statistics Statistik (DE-588)4056995-0 gnd Grenzwertsatz (DE-588)4158163-5 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Teoremas limites Teoria assintótica (inferência estatística) Limit theorems (Probability theory) Mathematical statistics Statistik Grenzwertsatz Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016813010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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