A class of robust and fully efficient regression estimators

Annals of Statistics

Volumn 30, Issue 2, 2002, Pages 583-616

  Gervini, Daniel ^a   Yohai, Víctor J ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Adaptive estimation; Efficient estimation; Maximum breakdown point; Weighted least squares

Indexed keywords

EID: 0036282009     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1021379866     Document Type: Article

References (18)

1. ADROVER, J., BIANCO, A. and YOHAI, V. J. (2001). Approximate τ-estimates for linear regression based on subsampling of elemental sets. In Statistics in Genetics and in the Environmental Sciences (L. T. Femholz, S. Morgenthaler and W. Stahel, eds.) 141-151. Birkäuser, Basel.
2. AGOSTINELLI, C. and MARKATOU, M. (1998). A one-step robust estimator for regression based on the weighted likelihood reweighting scheme. Statist. Probab. Lett. 37 341-350.
3. DAVIES, L. (1990). The asymptotics of S-estimators in the linear regression model. Ann. Statist. 18 1651-1675.
4. DONOHO, D. L. and HUBER, P. J. (1983). The notion of breakdown point. In A Festschrift for Erich L. Lehmann (P. J. Bickel, K. A. Doksum and J. L. Hodges, Jr., eds.) 157-184. Wadsworth, Belmont, CA.
5. GERVINI, D. and YOHAI, V. J. (2000). A class of robust and fully efficient regression estimators. Unpublished manuscript.
6. HAMPEL, F. R. (1975). Beyond location parameters: robust concepts and methods (with discussion). Bull. ISI 46 375-391.
7. HAMPEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J. and STAHEL, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.
8. HE, X. and PORTNOY, S. (1992). Reweighted LS estimators converge at the same rate as the initial estimator. Ann. Statist. 20 2161-2167.
9. HÖSSJER, O. (1992). On the optimality of S-estimators. Statist. Probab. Lett. 14 413-419.
10. MARTIN, R. D., YOHAI, V. J. and ZAMAR, R. H. (1989). Min-max bias robust regression. Ann. Statist. 17 1608-1630.
11. POLLARD, D. (1990). Empirical Processes: Theory and Applications. IMS, Hayward, CA.
12. ROUSSEEUW, P. J. (1984). Least median of squares regression. J. Amer. Statist. Assoc. 79 871-880.
13. ROUSSEEUW, P. J. and LEROY, A. (1987). Robust Regression and Outlier Detection. Wiley, New York.
14. ROUSSEEUW, P. J. and YOHAI, V. (1984). Robust regression by means of 5-estimators. Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. 26 256-272. Springer, New York.
15. SIMPSON, D. G. and YOHAI, V. J. (1998). Functional stability of one-step GM-estimators in approximately linear regression. Ann. Statist. 26 1147-1169.
16. YOHAI, V. J. (1987). High breakdown-point and high efficiency robust estimates for regression. Ann. Statist. 15 642-656.
17. YOHAI, V. J. and ZAMAR, R. H. (1988). High breakdown-point estimates of regression by means of the minimization of an efficient scale. J. Amer. Statist. Assoc. 83 406-413.
18. YOHAI, V. J. and ZAMAR, R. H. (1993). A minimax-bias property of the least a-quantile estimates. Ann. Statist. 21 1824-1842.