Handbook of Statistics, Volume 15: Robust Inference

G.S. Maddala, C.R. Rao0444821724, 9780444821720

This reference work covers the many aspects of Robust Inference. Much of what is contained in the chapters, written by leading experts in the field, has not been part of previous surveys of this area. Robust Inference has been an active area of research for the last two decades. Especially during recent years it has been extended in different directions covering a wide variety of models. This volume will be valuable for both graduate students and researchers using statistical methods.

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Table of contents :
Front cover……Page 1
Series……Page 2
Title page……Page 3
Date-line……Page 4
Preface……Page 5
Table of Contents……Page 7
Contributors……Page 15
1. Introduction……Page 19
2. Assumptions……Page 21
3. Main theorems……Page 22
4. Preliminary lemmas……Page 25
5. Proofs of main theorems……Page 28
6. Comments on difference of two convex functions……Page 31
7. Appendix, extensions of Rockafellar’s theorems……Page 32
Acknowledgement……Page 35
References……Page 36
1. Introduction……Page 39
2. Minimum Hellinger distance estimation……Page 40
3. Minimum disparity estimation……Page 50
4. The negative exponential disparity……Page 57
5. The weighted likelihood equation……Page 59
6. A generalized divergence……Page 63
References……Page 64
1. Introduction……Page 67
2. Approaches to robustness……Page 68
3. Robust tests for general parametric models……Page 75
4. Applications……Page 77
5. Other techniques……Page 85
6. Conclusions……Page 89
References……Page 90
1. Introduction……Page 95
2. Robustness concepts and results in testing……Page 96
3. Robust testing in logistic regression……Page 99
4. Robust model choice tests……Page 108
5. Conclusion……Page 113
Appendix……Page 114
References……Page 116
1. Motivation……Page 119
2. The breakdown value……Page 121
3. Positive-breakdown regression……Page 122
4. Detecting leverage points with the MVE……Page 125
5. Diagnostic display……Page 128
6. Substantive applications……Page 130
7. Other robust methods……Page 131
9. Algorithms……Page 133
10. Perspective and outlook……Page 134
References……Page 135
1. Introduction……Page 141
2. Outlier models……Page 143
3. Outlier identification rules……Page 147
4. Performance criteria for outlier identification rules……Page 151
5. A comparison of some specific outlier identification rules……Page 152
References……Page 159
1. Introduction……Page 163
2. Rank-based analysis……Page 164
3. Analyses based on GR-estimates……Page 174
4. Rank-based coefficients of determination……Page 178
5. Diagnostic procedures……Page 181
References……Page 189
1. Introduction……Page 193
2. Regression quantiles and rank scores……Page 200
3. Rank tests for heteroscedasticity……Page 204
4. Rank tests for time series models……Page 208
References……Page 215
1. Introduction……Page 219
2. Relations for single moments……Page 222
3. Relations for product moments……Page 226
5. Sensitivity of robust linear estimators of $theta$ under multiple-outlier exponential model……Page 236
6. Examples……Page 242
8. Results for two related sets of I.NI.D. variables……Page 243
9. Robustness of location estimation of double exponential distribution……Page 245
10. Robustness of scale estimators of double exponential distribution……Page 249
11. Illustrative example……Page 250
References……Page 252
1. Introduction……Page 255
2. Outlier detection in time series models……Page 256
3. Effects of outliers on unit root tests……Page 261
4. Robust unit root tests……Page 270
5. Robust estimation methods for non-stationary data……Page 276
6. Outliers and nonlinearities in time series……Page 278
References……Page 280
1. Introduction……Page 285
2. Inference based on the sample mean……Page 286
3. Inference on linear regression……Page 292
4. Inference based on robust estimates……Page 296
5. Inference in econometric models……Page 298
6. Bandwidth selection……Page 302
7. High-order asymptotics and the bootstrap……Page 304
8. Inference under long range dependence……Page 306
9. Inference on nonparametric probability density and regression functions……Page 309
References……Page 312
1. Introduction……Page 317
2. HAC covariance matrix estimators step by step……Page 319
3. Asymptotic properties……Page 327
4. Choices for kernel-based estimators……Page 337
5. Choices for parametric estimators……Page 350
6. Concluding comments……Page 357
References……Page 358
1. Mixed linear models……Page 361
2. Robustness in mixed linear models……Page 365
3. Estimation by maximising the Gaussian likelihood……Page 368
4. Estimation by maximising the student $t$ likelihood……Page 371
5. Estimation by maximising a robustified likelihood……Page 376
6. Estimation by solving estimating equations……Page 379
7. B-optimal estimation……Page 383
8. Estimation by maximusing the restricted Gaussian likelihood (REML)……Page 384
9. Robust versions of the restricted likelihood approach……Page 387
10. Estimators defined by algorithms……Page 392
11. Approximate inference……Page 396
12. Empirical experience……Page 400
References……Page 401
2. NPML estimation in semiparametric models……Page 403
3. NPMLE for censored and truncated data……Page 405
4. Discrete choice models……Page 407
5. Censored regression models……Page 410
6. Models for duration data……Page 412
7. Estimation from endogenously stratified samples……Page 416
8. Empirical likelihood ratio……Page 419
References……Page 421
1. Censored quantile regressions: An overview……Page 423
2. Asymptotic results on censored quantile regressions……Page 431
3. Interpolation property and algorithms……Page 441
4. Application: Earnings function……Page 448
References……Page 453
1. Introduction……Page 457
2. Identification analysis……Page 460
3. Estimation, confidence intervals and hypothesis tests……Page 466
4. Empirical examples……Page 473
5. Regression analysis with contaminated and corrupted data……Page 474
Appendix……Page 477
References……Page 483
1. Introduction……Page 485
2. $M$-estimators……Page 487
3. $L$-estimators……Page 498
4. $R$-estimation of location and regression……Page 508
5. Minimum distance $P$- and $B$- estimators……Page 518
6. Interrelations of robust estimators……Page 519
7. Concluding remarks……Page 524
References……Page 528
1. Introduction……Page 531
2. General approach……Page 533
3. Approximations for M-estimates……Page 534
4. General saddlepoint approximations……Page 538
5. Marginal densities: $M$-estimates……Page 541
6. Marginal densities: General……Page 542
7. Estimation of tail areas……Page 544
8. Confidence intervals……Page 546
9. Comparison of empirical techniques……Page 551
10. Conclusions……Page 552
References……Page 553
1. Introduction……Page 555
2. Comments on breakdown points……Page 557
3. Comments on influence function (IF)……Page 561
4. Empirical robustness……Page 565
References……Page 567
1. Introduction……Page 569
2. One-sample problems……Page 572
3. $K$-sample problems……Page 586
4. Tests of independence……Page 595
5. Factorial designs……Page 597
6. Regression models……Page 602
Truncation Programs……Page 624
References……Page 634
1. Introduction……Page 651
2. Formal reflection of diversity of estimates……Page 653
3. Estimating contamination level……Page 654
4. Robust testing……Page 657
References……Page 660
1. Introduction……Page 663
2. Group invariance……Page 667
3. The general linear hypothesis (MANOVA problem)……Page 669
4. Robustness of tests on $Sigma$……Page 672
5. Tests for serial correlation……Page 674
6. One-sided testing problem……Page 676
References……Page 678
2. Some comments on diagnostics and robust methods……Page 679
4. Generalized distributions……Page 681
5. Robust inference in logistic and censored regression models……Page 682
7. Panel data……Page 683
8. Multivariate methods and simultaneous equations models……Page 684
9. Bootstrap methods for small-sample inference……Page 685
10. Robust Bayesian analysis……Page 686
References……Page 688
Subject Index……Page 695
Contents of Previous Volumes……Page 701
Back cover……Page 717