Asymptotic efficiency of nonparametric tests:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 274 S. |
| ISBN: | 0521470293 9780521470292 9780521115926 |
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| 245 | 1 | 0 | |a Asymptotic efficiency of nonparametric tests |c Yakov Nikitin |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XVI, 274 S. | ||
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Contents
Introduction page ix
1 Asymptotic Efficiency of Statistical Tests and
Mathematical Means for Its Computation 1
1.1 General Approach to Computation of Asymptotic
Efficiency 1
1.2 Bahadur Asymptotic Relative Efficiency 4
1.3 Hodges Lehmann Asymptotic Relative Efficiency 13
1.4 Pitman Asymptotic Relative Efficiency 15
1.5 Different Approaches to the Definition of the ARE 18
1.6 Some Results on Probabilities of Large Deviations 21
1.7 On Large Deviations of Empirical Measures in the
Case of Several Independent Samples 33
1.8 Some Results from the Theory of Extremal Problems
and the Theory of Implicit Operators 36
2 Asymptotic Efficiency of Nonparametric
Goodness of Fit Tests 40
2.1 Problem Statement and Tests under Consideration 40
2.2 Large Deviations of Kolmogorov Smirnov Type Statistics 42
2.3 Large Deviations of Integral Statistics. Euler Lagrange
Equations 50
2.4 Large Deviations of Integral Statistics.
Constructing Solutions of the Euler Lagrange
Equations 57
2.5 Large Deviations of Integral Anderson Darling, Watson,
and Khmaladze Aki Statistics 66
v
vi Contents
2.6 Bahadur Efficiency of Goodness of Fit Tests 73
2.7 Hodges Lehmann ARE of Goodness of Fit Tests 81
2.8 Hodges Lehmann and Chernoff Efficiencies of the
Smirnov Statistic 89
3 Asymptotic Efficiency of Nonparametric
Homogeneity Tests 94
3.1 Problem Statement and Tests under Consideration 94
3.2 Large Deviations of Integral Two Sample Statistics 97
3.3 Bahadur Efficiency of Homogeneity Tests 101
3.4 Hodges Lehmann Efficiency of Homogeneity Tests 105
3.5 Hodges Lehmann and Chernoff Efficiencies of Linear
Rank Tests 109
3.6 Asymptotic Comparison of Tests in Problems of Signal
Detection in Noise of Unknown Level 120
4 Asymptotic Efficiency of Nonparametric
Symmetry Tests 127
4.1 Problem Statement and Tests under Consideration 127
4.2 Large Deviations of Kohnogorov Type and Signed Rank
Statistics 130
4.3 Large Deviations of Integral Statistics for
Testing Symmetry 136
4.4 Bahadur Efficiency of Symmetry Tests 143
4.5 Hodges Lehmann Efficiency of Symmetry Tests 147
4.6 Hodges Lehmann and Chernoff Efficiencies of the Sign
and the Wilcoxon Statistics 151
4.7 Hodges Lehmann and Chernoff Efficiencies of Linear
Signed Rank Tests 155
4.8 Approximate Bahadur and Pitman Efficiencies
of Symmetry Tests 164
5 Asymptotic Efficiency of Nonparametric
Independence Tests 169
5.1 Problem Statement and Tests under Consideration 169
5.2 Large Deviations of Kohnogorov Type Statistics 171
5.3 Large Deviations of Integral Statistics for Independence
Testing 181
5.4 Bahadur Efficiency of Independence Tests 190
5.5 Large Deviations of Statistics for Testing Uniformity on
a Square 196
t
Contents vii
5.6 Local Exact Slopes 202
5.7 Hodges Lehmann Efficiency of Independence Tests 205
6 Local Asymptotic Optimality of Nonparametric
Tests and the Characterization of Distributions 208
6.1 Introduction and Statement of the Problem 208
6.2 Domains of the Bahadur Local Asymptotic Optimality
(LAO) of Goodness of Fit Tests 211
6.3 Characterization of Distributions by the LAO Property
of Goodness of Fit Tests under Concrete Alternatives 222
6.4 The LAO Domains for Homogeneity Tests 231
6.5 The LAO Domains for Symmetry Tests 238
6.6 The LAO Domains for Independence Tests 241
Bibliography 249
Index 265 |
| any_adam_object | 1 |
| author | Nikitin, Jakov |
| author_GND | (DE-588)1067604693 |
| author_facet | Nikitin, Jakov |
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| discipline | Mathematik |
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| id | DE-604.BV010517946 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-17T12:02:02Z |
| institution | BVB |
| isbn | 0521470293 9780521470292 9780521115926 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007011171 |
| oclc_num | 832424766 |
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| owner_facet | DE-12 DE-739 DE-706 DE-11 DE-188 DE-824 |
| physical | XVI, 274 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Nikitin, Jakov Verfasser (DE-588)1067604693 aut Asymptotic efficiency of nonparametric tests Yakov Nikitin 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 XVI, 274 S. txt rdacontent n rdamedia nc rdacarrier Nichtparametrischer Test (DE-588)4075372-4 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Asymptotische Wirksamkeit (DE-588)4131644-7 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 s Asymptotische Wirksamkeit (DE-588)4131644-7 s DE-604 Nichtparametrischer Test (DE-588)4075372-4 s DE-188 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007011171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nikitin, Jakov Asymptotic efficiency of nonparametric tests Nichtparametrischer Test (DE-588)4075372-4 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Asymptotische Wirksamkeit (DE-588)4131644-7 gnd |
| subject_GND | (DE-588)4075372-4 (DE-588)4226777-8 (DE-588)4131644-7 |
| title | Asymptotic efficiency of nonparametric tests |
| title_auth | Asymptotic efficiency of nonparametric tests |
| title_exact_search | Asymptotic efficiency of nonparametric tests |
| title_full | Asymptotic efficiency of nonparametric tests Yakov Nikitin |
| title_fullStr | Asymptotic efficiency of nonparametric tests Yakov Nikitin |
| title_full_unstemmed | Asymptotic efficiency of nonparametric tests Yakov Nikitin |
| title_short | Asymptotic efficiency of nonparametric tests |
| title_sort | asymptotic efficiency of nonparametric tests |
| topic | Nichtparametrischer Test (DE-588)4075372-4 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Asymptotische Wirksamkeit (DE-588)4131644-7 gnd |
| topic_facet | Nichtparametrischer Test Nichtparametrische Statistik Asymptotische Wirksamkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007011171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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