A Class of Locally and Globally Robust Regression Estimates

References

• Carroll , R. J. and Ruppert , D. 1985 . “Transformations in Regression. A Robust Analysis,” . Technometrics , 27 : 1 – 12 .
   Web of Science ®Google Scholar
• Coakley , C. W. and Hettmansperger , T. P. 1993 . “A Bounded Influence, High-Breakdown, Efficient Regression Estimator,” . Journal of the American Statistical Association , 88 : 872 – 880 .
   Web of Science ®Google Scholar
• Donoho , D. L. 1982 . “Breakdown Properties of Multivariate Location Estimators,” , Harvard University . Ph.D. qualifying paper
   Google Scholar
• Ferretti , N. , Kelmansky , D. , Yohai , V. J. and Zamar , R. H. 1996 . “Generalized Estimates,” , University of British Columbia, Dept. of Statistics . Technical Report 164
   Google Scholar
• Hampel , F. R. 1971 . “A General Qualitative Definition of Robustness,” . Annals of Mathematical Statistics , 42 : 1887 – 1896 .
   Google Scholar
• Hampel , F. R. 1974 . “The Influence Function and Its Role in Robust Estimation,” . Journal of the American Statistical Association , 69 : 383 – 393 .
   Web of Science ®Google Scholar
• Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. A. 1986 . Robust Statistics: The Approach Based on Influence Functions , New York : Wiley .
   Google Scholar
• Hawkins , D. M. , Simonoff , J. S. and Stromberg , A. J. 1994 . “Distributing a Computationally Intensive Estimator: The Case of Exact LMS Regression,” . Computational Statistics , 9 : 83 – 95 .
   Web of Science ®Google Scholar
• He , X. 1991 . “A Local Breakdown Property of Robust Tests in Linear Regression,” . Journal of Multivariate Analysis , 38 : 294 – 305 .
   Web of Science ®Google Scholar
• He , X. and Simpson , D. G. 1992 . “Robust Direction Estimation,” . The Annals of Statistics , 20 : 351 – 369 .
   Web of Science ®Google Scholar
• He , X. and Simpson , D. G. 1993 . “Lower Bounds for Contamination Bias: Globally Minimax Versus Locally Linear Estimation,” . The Annals of Statistics , 21 : 314 – 337 .
   Web of Science ®Google Scholar
• Krasker , W. S. 1980 . “Estimation of a Linear Regression Model With Disparate Data Points,” . Econometrica , 48 : 1333 – 1346 .
   Web of Science ®Google Scholar
• Krasker , W. S. and Welsch , R. E. 1982 . “Efficient Bounded Influence Regression Estimation,” . Journal of the American Statistical Association , 77 : 595 – 604 .
   Web of Science ®Google Scholar
• Maronna , R. A. , Bustos , O. H. and Yohai , V. J. 1979 . “Bias and Efficiency Robustness of General M-Estimators for Regression With Random Carries,” . In Smoothing Techniques for Curve Estimation , Edited by: Gasser , T. and Rosenblatt , M. 91 – 116 . Berlin : Springer . Lecture Notes in Mathematics 757
   Google Scholar
• Maronna , R. A. , Stahel , W. A. and Yohai , V. J. 1992 . “Bias-Robust Estimators of Multivariate Scatter Based on Projections,” . Journal of Multivariate Analysis , 42 : 141 – 161 .
   Web of Science ®Google Scholar
• Maronna , R. A. and Yohai , V. J. 1993 . “Bias-Robust Estimates of Regression Based on Projections,” . The Annals of Statistics , 21 : 965 – 990 .
   Web of Science ®Google Scholar
• Maronna , R. A. and Yohai , V. J. 1995 . “The Behavior of the Stahel–Donoho Robust Multivariate Estimator,” . Journal of the American Statistical Association , 90 : 330 – 341 .
   Web of Science ®Google Scholar
• Martin , R. D. , Yohai , V. J. and Zamar , R. H. 1989 . “Min-Max Bias Robust Regression,” . The Annals of Statistics , 17 : 1608 – 1630 .
   Web of Science ®Google Scholar
• Rousseeuw , P. J. 1984 . “Least Median of Squares Regression,” . Journal of the American Statistical Association , 79 : 871 – 880 .
   Web of Science ®Google Scholar
• Rousseeuw , P. J. 1993 . “A Resampling Design for Computing High-Breakdown Regression,” . Statistics and Probability Letters , 18 : 125 – 128 .
   Web of Science ®Google Scholar
• Rousseeuw , P. J. and Leroy , A. M. 1987 . Robust Regression and Outlier Detection , New York : Wiley .
   Google Scholar
• Rousseeuw , P. J. and Yohai , V. J. 1984 . “Robust Regression by Means of S Estimators,” . In Robust and Nonlinear Time Series Analysis , Edited by: Franke , J. , Härdle , W. and Martin , R. D. 256 – 272 . New York : Springer-Verlag . Lecture Notes in Statistics 26
   Google Scholar
• Ruppert , D. and Carroll , R. J. 1980 . “Trimmed Least Squares Estimation in the Linear Model,” . Journal of the American Statistical Association , 75 : 828 – 838 .
   Web of Science ®Google Scholar
• Simpson , D. G. , Ruppert , D. and Carroll , R. J. 1992 . “On One-Step GM Estimates and Stability of Inferences in Linear Regression Model,” . Journal of the American Statistical Association , 87 : 439 – 450 .
   Web of Science ®Google Scholar
• Simpson , D. G. and Yohai , V. J. 1998 . “Functional Stability of One-Step GM Estimators in Linear Regression,” . The Annals of Statistics , 26 : 1147 – 1169 .
   Google Scholar
• Stahel , W. A. 1981 . “Robuste Schätzungen: Infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen,” , Ph.D. dissertation Zürich : ETH .
   Google Scholar
• Stromberg , A. J. 1993 . “Computing the Exact Least Median of Squares Estimate and Stability Diagnostics in Multiple Linear Regression,” . SIAM Journal on Scientific Computing , 14 : 1289 – 1299 .
   Web of Science ®Google Scholar
• Yohai , V. J. 1987 . “High–Breakdown Point and High-Efficiency Robust Estimates for Regression,” . The Annals of Statistics , 15 : 642 – 656 .
   Web of Science ®Google Scholar
• Yohai , V. J. and Zamar , R. H. 1988 . “High Breakdown–Point Estimates of Regression by Means of the Minimization of an Efficient Scale,” . Journal of the American Statistical Association , 83 : 406 – 413 .
   Web of Science ®Google Scholar
• Yohai , V. J. and Zamar , R. H. 1993 . “A Minimax-Bias Property of the Least Alpha-Quantile Estimates,” . The Annals of Statistics , 21 : 1824 – 1842 .
   Google Scholar
• Yohai , V. J. and Zamar , R. H. 1997 . “Optimal Locally Robust Regression Estimates,” . Journal of Statistical Planning and Inference , 66 : 309 – 323 .
   Google Scholar