Robust statistical procedures: asymptotics and interrelations
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1996
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Publisher description Table of Contents Inhaltsverzeichnis |
| Physical Description: | XIV, 466 S. |
| ISBN: | 0471822213 |
Staff View
MARC
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| 245 | 1 | 0 | |a Robust statistical procedures |b asymptotics and interrelations |c Jana Jurečková ; Pranab Kumar Sen |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1996 | |
| 300 | |a XIV, 466 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 7 | |a estimateur |2 inriac | |
| 650 | 7 | |a statistique robuste |2 inriac | |
| 650 | 4 | |a Robust statistics | |
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Record in the Search Index
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| adam_text | Contents
Preface
xi
Acknowledgments
xiii
1
Introduction and Synopsis
1
1.1
Introduction
1
1.2
Synopsis
7
PART I ASYMPTOTICS AND INTERRELATIONS
2
Preliminaries
15
2.1
Introduction
15
2.2
Inference in Linear Models
15
2.3
Robustness Concepts
21
2.3.1
Finite-Sample Breakdown and Tail-Performance
26
2.4
Robust and Minimax Estimation of Location
32
2.5
Clippings from Probability and Asymptotic Theory
36
2.5.1
Modes of Convergence of Stochastic Elements
38
2.5.2
Basic Probability Inequalities
41
2.5.3
Some Useful Inequalities and Lemmas
43
2.5.4
Laws of Large Numbers and Related Inequalities
48
2.5.5
Central Limit Theorems
50
2.5.6
Limit Theorems Allied to CLTs
56
2.5.7
CLTs for Quadratic Forms
59
2.5.8
Contiguity of Probability Measures
60
2.5.9
Hájek-Inagaki-LeCam
Theorem and the LAN
Condition
61
U
CONTENTS
2.5.10
Weak
Convergence
of Probability Measures
62
2.5.11
Some Important Gaussian Functions
66
2.5.12
Weak
Invariance
Principles
68
2.5.13
Empirical Distributional Processes
70
2.5.14
Weak
Invariance
Principle: Random Change
of Time
73
2.5.15
Embedding Theorems and Strong
Invariance
Principles
73
2.5.16
Asymptotic Relative Efficiency: Concept and
Measures
76
2.6
Problems
77
3
Robust Estimation of Location and Regression
79
3.1
Introduction
79
3.2
M-Estimators
80
3.3
L-Estimators
88
3.4
R-Estimators
102
3.5
Minimum Distance and Pitman Estimators
113
3.5.1
Minimum Distance Estimation
114
3.5.2
Pitman Estimators
115
3.5.3
Pitman-Type Estimators of Location
116
3.5.4
Bayes-Type Estimators of General Parameter
117
3.6
Differentiable Statistical Functions
118
3.7
Problems
126
4
Asymptotic Representations for L-Estimators
135
4.1
Introduction
135
4.2
Bahadur s Representations for Sample Quantiles
138
4.3
Representations for Smooth Scores L-Statistics
142
4.4
Asymptotic Representations for General L-Estimators
149
4.5
Representations for Statistical Functionals
150
4.6
SOADR for Certain Smooth L-Functionals
156
4.7
L-Estimation in Linear Model
163
4.8
Breakdown Point of Some L-and M-Estimators
176
4.9
Problems
179
5
Asymptotic Representations for M-Estimators
183
5.1
Introduction
183
5.2
M-Estimation of General Parameters
184
5.3
M-Estimation of Location: Fixed Scale
191
5.3.1
Possibly Discontinuous but Monotone
ψ
196
CONTENTS jx
5.3.2
Possible
Discontinuous and
Nonmonotone
ψ
197
5.3.3
Second-Order Distributional Representations
201
5.4
Studentized M-Estimators of Location
206
5.5
M-Estimation in Linear Regression Model
215
5.6
Some Studentizing Scale Statistics for Linear Models
224
5.7
Hadamard
Differentiability Approaches for
M-Estimators in Linear Models
227
5.8
Problems
231
6
Asymptotic Representations for R-Estimators
235
6.1
Introduction
235
6.2
First Order Representations for R-Estimators of Location
236
6.3
SO ADR for R-Estimators of Location
244
6.4
Representations for R-Estimators of Regression
252
6.5
SOADR for Regression R-Estimators
263
6.6
Representations for R-Estimators in Linear Model
268
6.7
Regression Rank Scores
275
6.7.1
Asymptotic Representation of RR-Process
278
6.7.2
Asymptotics for RR-Estimators
282
6.8
Studentizing Scale Statistic and Regression Rank Scores
285
6.9
Problems
287
7
Asymptotic Interrelations of Estimators
291
7.1
Introduction
291
7.2
Asymptotic Interrelations of Location Estimators
293
7.2.1
Asymptotic Relations of Location M- and
L-Estimators
294
7.2.2
Asymptotic Relations of Location M- and
R-Estimators
301
7.2.3
Asymptotic Relations of Location L- and
R-Estimators
303
7.3
Asymptotic Relations in the Linear Model
304
7.3.1
M-and R-Estimators
304
7.3.2
Asymptotic Relations of Huber s M-Estimator
and Trimmed
LSE
in the Linear Model
306
7.4
Approximation By One-Step Versions
307
7.4.1
One-Step Version of General M-Estimator
308
7.4.2
One-Step Version of M-Estimator of Location
312
7.4.3
One-Step Versions in Linear Models
318
7.5
Problems
321
X
CONTENTS
PART II ROBUST STATISTICAL INFERENCE
8
Robust Sequential and Recursive Point Estimation
325
8.1
Introduction
325
8.2
Minimum Risk Estimation
327
8.3
AMRE of Stein-Rule Estimators
338
8.4
Recursive and K-Step Estimators
352
8.5
Robust Adaptive Estimation
359
8.6
Problems
365
9
Robust Confidence Sets and Intervals
367
9.1
Introduction
367
9.2
Type I and II Confidence Intervals
369
9.3
Multiparameter Confidence Sets
387
9.4
Bounded-Width Confidence Intervals
394
9.5
Sequential Confidence Sets
400
9.6
Some General Remarks
402
9.7
Problems
403
10
Robust Statistical Tests
407
10.1
Introduction
407
10.2
M-Tests
408
10.3
R-Tests
416
10.4
Concluding Notes on Robust Tests
418
10.5
Problems
421
Appendix A
423
АЛ
Introduction
423
A.2 Uniform Asymptotic Linearity
423
A.3
Hadamard
Differentiability of Regression Functional
428
A.4 Problems
432
References
433
Author Index
459
Subject Index
463
|
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| author | Jurečková, Jana 1940- Sen, Pranab Kumar 1937- |
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| author_facet | Jurečková, Jana 1940- Sen, Pranab Kumar 1937- |
| author_role | aut aut |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/4 519.5/4 20 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Jurečková, Jana 1940- Verfasser (DE-588)122145259 aut Robust statistical procedures asymptotics and interrelations Jana Jurečková ; Pranab Kumar Sen New York [u.a.] Wiley 1996 XIV, 466 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Non-parametrische statistiek gtt Statistiques robustes ram Stochastische modellen gtt analyse asymptotique inriac estimateur inriac statistique robuste inriac Robust statistics Robuste Statistik (DE-588)4451047-0 gnd rswk-swf Robuste Schätzung (DE-588)4178265-3 gnd rswk-swf Robuste Statistik (DE-588)4451047-0 s DE-604 Robuste Schätzung (DE-588)4178265-3 s Sen, Pranab Kumar 1937- Verfasser (DE-588)124306942 aut http://www.loc.gov/catdir/description/wiley034/95017912.html Publisher description http://www.loc.gov/catdir/toc/onix05/95017912.html Table of Contents Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007206797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jurečková, Jana 1940- Sen, Pranab Kumar 1937- Robust statistical procedures asymptotics and interrelations Non-parametrische statistiek gtt Statistiques robustes ram Stochastische modellen gtt analyse asymptotique inriac estimateur inriac statistique robuste inriac Robust statistics Robuste Statistik (DE-588)4451047-0 gnd Robuste Schätzung (DE-588)4178265-3 gnd |
| subject_GND | (DE-588)4451047-0 (DE-588)4178265-3 |
| title | Robust statistical procedures asymptotics and interrelations |
| title_auth | Robust statistical procedures asymptotics and interrelations |
| title_exact_search | Robust statistical procedures asymptotics and interrelations |
| title_full | Robust statistical procedures asymptotics and interrelations Jana Jurečková ; Pranab Kumar Sen |
| title_fullStr | Robust statistical procedures asymptotics and interrelations Jana Jurečková ; Pranab Kumar Sen |
| title_full_unstemmed | Robust statistical procedures asymptotics and interrelations Jana Jurečková ; Pranab Kumar Sen |
| title_short | Robust statistical procedures |
| title_sort | robust statistical procedures asymptotics and interrelations |
| title_sub | asymptotics and interrelations |
| topic | Non-parametrische statistiek gtt Statistiques robustes ram Stochastische modellen gtt analyse asymptotique inriac estimateur inriac statistique robuste inriac Robust statistics Robuste Statistik (DE-588)4451047-0 gnd Robuste Schätzung (DE-588)4178265-3 gnd |
| topic_facet | Non-parametrische statistiek Statistiques robustes Stochastische modellen analyse asymptotique estimateur statistique robuste Robust statistics Robuste Statistik Robuste Schätzung |
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