Robust statistics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2009
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| Edition: | 2. ed. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 354 S. graph. Darst. |
| ISBN: | 9780470129906 |
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MARC
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| 245 | 1 | 0 | |a Robust statistics |c Peter J. Huber ; Elvezio M. Ronchetti |
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Record in the Search Index
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| adam_text | Titel: Robust statistics
Autor: Huber, Peter J.
Jahr: 2009
CONTENTS
Preface xiii
Preface to First Edition XV
1 Generalities 1
1.1 Why Robust Procedures ? I
1.2 What Should a Robust Procedure Achieve? 5
1.2.1 Robust. Nonparametric. and Distribution-Free 6
1.2.2 Adaptive Procedures 7
1.2.3 Resistant Procedures 8
1.2.4 Robustness versus Diagnostics 8
1.2.5 Breakdown point 8
1.3 Qualitative Robustness 9
1.4 Quantitative Robustness II
1.5 Infinitesimal Aspects 14
1.6 Optimal Robustness 17
1.7 Performance Comparisons 18
Viii CONTENTS
1.8 Computation of Robust Estimates 18
1.9 Limitations to Robustness Theory 20
2 The Weak Topology and its Metrization 23
2.1 General Remarks 23
2.2 The Weak Topology 23
2.3 Levy and Prohorov Metrics 27
2.4 The Bounded Lipschitz Metric 32
2.5 Fréchet and Gâteaux Derivatives 36
2.6 Hampel s Theorem 41
3 The Basic Types of Estimates 45
3.1 General Remarks 45
3.2 Maximum Likelihood Type Estimates (M-Estimates) 46
3.2.1 Influence Function of M-Estimates 47
3.2.2 Asymptotic Properties of M-Estimates 48
3.2.3 Quantitative and Qualitative Robustness of M-
Estimates 53
3.3 Linear Combinations of Order Statistics (X-Estimates) 55
3.3.1 Influence Function of L-Estimates 56
3.3.2 Quantitative and Qualitative Robustness of L-Estimates 59
3.4 Estimates Derived from Rank Tests (ñ-Estimates) 60
3.4.1 Influence Function of /¿-Estimates 62
3.4.2 Quantitative and Qualitative Robustness of ^-Estimates 64
3.5 Asymptotically Efficient M-, L-, and .fi-Estimates 67
4 Asymptotic Minimax Theory for Estimating Location 71
4.1 General Remarks 71
4.2 Minimax Bias 72
4.3 Minimax Variance: Preliminaries 74
4.4 Distributions Minimizing Fisher Information 76
4.5 Determination of Fo by Variational Methods 81
4.6 Asymptotically Minimax A/-Estimates 91
4.7 On the Minimax Property for L- and Ä-Estimates 95
4.8 Redescending A/-Estimates 97
4.9 Questions of Asymmetric Contamination 101
CONTENTS IX
Scale Estimates 105
5.1 General Remarks 105
5.2 M-Estimates of Scale 107
5.3 L-Estimates of Scale 109
5.4 .¿¿-Estimates of Scale 112
5.5 Asymptotically Efficient Scale Estimates 114
5.6 Distributions Minimizing Fisher Information for Scale 115
5.7 Minimax Properties 119
6 Multiparameter Problems—in Particular Joint Estimation
of Location and Scale 125
6.1 General Remarks 125
6.2 Consistency of M-Estimates 126
6.3 Asymptotic Normality of M-Estimates 130
6.4 Simultaneous M-Estimates of Location and Scale 133
6.5 M -Estimates with Preliminary Estimates of Scale 137
6.6 Quantitative Robustness of Joint Estimates of Location and Scale 139
6.7 The Computation of M-Estimates of Scale 143
6.8 Studentizing 145
7 Regression 149
7.1 General Remarks 149
7.2 The Classical Linear Least Squares Case 154
7.2.1 Residuals and Outliers 158
7.3 Robustizing the Least Squares Approach 160
7.4 Asymptotics of Robust Regression Estimates 163
7.4.1 The Cases hp2 - 0 and hp - 0 164
7.5 Conjectures and Empirical Results 168
7.5.1 Symmetric Error Distributions 168
7.5.2 The Question of Bias 168
7.6 Asymptotic Covariances and Their Estimation 170
7.7 Concomitant Scale Estimates 172
7.8 Computation of Regression M-Estimates 175
7.8.1 The Scale Step 176
7.8.2 The Location Step with Modified Residuals 178
7.8.3 The Location Step with Modified Weights 179
X CONTENTS
7.9 The Fixed Carrier Case: What Size ht ? 186
7.10 Analysis of Variance 190
7.11 ¿i-estimates and Median Polish 193
7.12 Other Approaches to Robust Regression 195
8 Robust Covariance and Correlation Matrices 199
8.1 General Remarks 199
8.2 Estimation of Matrix Elements Through Robust Variances 203
8.3 Estimation of Matrix Elements Through Robust Correlation 204
8.4 An Afflnely Equivariant Approach 210
8.5 Estimates Determined by Implicit Equations 212
8.6 Existence and Uniqueness of Solutions 214
8.6.1 The Scatter Estimate V 214
8.6.2 The Location Estimate t 219
8.6.3 Joint Estimation of t and V 220
8.7 Influence Functions and Qualitative Robustness 220
8.8 Consistency and Asymptotic Normality 223
8.9 Breakdown Point 224
8.10 Least Informative Distributions 225
8.10.1 Location 225
8.10.2 Covariance 227
8.11 Some Notes on Computation 233
9 Robustness of Design 239
9.1 General Remarks 239
9.2 Minimax Global Fit 240
9.3 Minimax Slope 246
10 Exact Finite Sample Results 249
10.1 General Remarks 249
10.2 Lower and Upper Probabilities and Capacities 250
10.2.1 2-Monotone and 2-Alternating Capacities 255
10.2.2 Monotone and Alternating Capacities of Infinite Order 258
10.3 Robust Tests 259
10.3.1 Particular Cases 265
10.4 Sequential Tests 267
CONTENTS XI
10.5 The Neyman-Pearson Lemma for 2-Alternating Capacities 269
10.6 Estimates Derived From Tests 272
10.7 Minimax Interval Estimates 276
11 Finite Sample Breakdown Point 279
11.1 General Remarks 279
11.2 Definition and Examples 281
11.2.1 One-dimensional Ai-estimators of Location 283
11.2.2 Multidimensional Estimators of Location 283
11.2.3 Structured Problems: Linear Models 284
II.2A Variances and Covariances 286
11.3 Infinitesimal Robustness and Breakdown 286
11.4 Malicious versus Stochastic Breakdown 287
12 Infinitesimal Robustness 289
12.1 General Remarks 289
12.2 Hampel s Infinitesimal Approach 290
12.3 Shrinking Neighborhoods 294
13 Robust Tests 297
13.1 General Remarks 297
13.2 Local Stability of a Test 298
13.3 Tests for General Parametric Models in the Multivariate Case 301
13.4 Robust Tests for Regression and Generalized Linear Models 304
14 Small Sample Asymptotics 307
14.1 General Remarks 307
14.2 Saddlepoint Approximation for the Mean 308
14.3 Saddlepoint Approximation of the Density of M-estimators 311
14.4 Tail Probabilities 313
14.5 Marginal Distributions 314
14.6 Saddlepoint Test 316
14.7 Relationship with Nonparametric Techniques 317
14.8 Appendix 321
XU CONTENTS
15 Bayesian Robustness 323
15.1 General Remarks 323
15.2 Disparate Data and Problems with the Prior 326
15.3 Maximum Likelihood and Bayes Estimates 327
15.4 Some Asymptotic Theory 329
15.5 Minimax Asymptotic Robustness Aspects 330
15.6 Nuisance Parameters 331
15.7 Why there is no Finite Sample Bayesian Robustness Theory 331
References 333
Index 345
|
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| author | Huber, Peter J. 1934- Ronchetti, Elvezio 1955- |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| institution | BVB |
| isbn | 9780470129906 |
| language | English |
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| physical | XVI, 354 S. graph. Darst. |
| publishDate | 2009 |
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| series2 | Wiley series in probability and statistics |
| spelling | Huber, Peter J. 1934- Verfasser (DE-588)112055745 aut Robust statistics Peter J. Huber ; Elvezio M. Ronchetti 2. ed. Hoboken, NJ Wiley 2009 XVI, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Robuste Statistik (DE-588)4451047-0 gnd rswk-swf Robuste Statistik (DE-588)4451047-0 s DE-604 Ronchetti, Elvezio 1955- Verfasser (DE-588)132529173 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020145202&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huber, Peter J. 1934- Ronchetti, Elvezio 1955- Robust statistics Robuste Statistik (DE-588)4451047-0 gnd |
| subject_GND | (DE-588)4451047-0 |
| title | Robust statistics |
| title_auth | Robust statistics |
| title_exact_search | Robust statistics |
| title_full | Robust statistics Peter J. Huber ; Elvezio M. Ronchetti |
| title_fullStr | Robust statistics Peter J. Huber ; Elvezio M. Ronchetti |
| title_full_unstemmed | Robust statistics Peter J. Huber ; Elvezio M. Ronchetti |
| title_short | Robust statistics |
| title_sort | robust statistics |
| topic | Robuste Statistik (DE-588)4451047-0 gnd |
| topic_facet | Robuste Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020145202&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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