A one-step robust estimator for regression based on the weighted likelihood reweighting scheme

Statistics and Probability Letters

Volumn 37, Issue 4, 1998, Pages 341-350

  Agostinelli, Claudio ^a   Markatou, Marianthi ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b Howard Hughes Medical Institute   (United States)

Author keywords

Breakdown point; Efficiency; Influence; Robust; Weighted likelihood

Indexed keywords

EID: 0032579671     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(97)00136-3     Document Type: Article

References (24)

1. Brownlee, K.A., 1965. Statistical Theory and Methodology in Science and Engineering, Wiley, New York.
2. Carroll, R.J., Ruppert, D., 1985. Transformations in regression; A robust analysis. Technometrics, 27, 1-12.
3. Coakley, C.W., Hettmansperger, T.P., 1993. A bounded influence, high breakdown, efficient regression estimator. J Amer. Statist. Assoc. 88, 872-880.
4. Donoho, D.L., 1982. Breakdown properties of multivariate location estimators. Ph.D. qualifying paper, Department of Statistics, Harvard University, Cambridge, MA.
5. Donoho, D.L., Huber, P.J., 1983. The notion of breakdown point, in: Bickel, P.J., Doksum, K., Hodges, J.L. Jr. (Eds.), Festschrift fur Erich L. Lehmann, Wadsworth, Belmont, CA, pp. 157-184.
6. Efron, B., Tibshirani, R., 1986. Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy. Statist. Sci. 1, 54-77.
7. Hampel, F.R., 1971. A general qualitative definition of robustness. Ann. Math. Statist. 42, 1887-1896.
8. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., 1986. Robust Statistics: The Approach based on Influence Functions, Wiley, New York.
9. He, X., 1991. A local breakdown property of robust tests in linear regression. J. Multivariate Anal. 38, 294-305.
10. He, X., Portnoy, S., 1992. Reweighted LS estimators converge at the same rate as the initial estimator. The Ann. Statist. 20, 2161-2167.
11. Hodges, J.L. Jr., 1967. Efficiency in normal samples and tolerance of extreme values for some estimators of location. In: Proc. 5th Berkeley Symp. on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, CA, pp. 163-186.
12. Huber, P.J., 1981. Robust Statistics, Wiley, New York.
13. Krasker, W.S., Welsch, R.E., 1982. Efficient bounded-influence regression estimation. J. Amer. Statist. Assoc. 77, 595-604.
14. Lindsay, B.G., 1994. Efficiency versus robustness: The case for minimum Hellinger distance and related methods. Ann. Statist. 22, 1018-1114.
15. Markatou, M., 1996. Robust statistical inference: weighted likelihoods or usual M-estimation? Commun. Statist. Theory and Methods 25, 2597-2613.
16. Markatou, M., Basu, A., Lindsay, B.G., 1995. Weighted likelihood estimating equations: the continuous case. Technical Report, Department of Statistics, Columbia University, New York.
17. Markatou, M., Basu, A., Lindsay, B.G , 1997. Weighted likelihood estimating equations: the discrete case with applications to logistic regression. J. Statist. Planning Inference 57, 215-232.
18. Montgomery, D.C., Peck, E.A., 1982. Introduction to Linear Regression Analysis, Wiley, New York.
19. Rousseeuw, P.J., Croux, C., 1993. Alternatives to the median absolute deviation. J. Amer. Statist. Assoc. 88, 1273-1283.
20. Rousseeuw, P.J., Leroy, A.M., 1987. Robust Regression and Outlier Detection, Wiley, New York.
21. Ruppert, D., 1992. Computing -estimators for regression and multivariate location/dispersion. J. Comput. Graphical Statist. 1, 253-270.
22. Ruppert, D., Carroll, R.J., 1980. Trimmed least squares estimation in the linear model. J. Amer. Statist. Assoc. 75, 828-838.
23. Simpson, D.G., Ruppert, D., Carroll, R.J., 1992. On one-step GM estimates and stability of inferences in linear regression. J. Amer. Statist. Assoc. 87, 439-450.
24. Welsh, A.H., Ronchetti, E., 1993. A failure of intuition: Naive outlier deletion in linear regression. Preprint.