On the explosion rate of maximum-bias functions

Canadian Journal of Statistics

Volumn 26, Issue 2, 1998, Pages 333-351

  Berrendero, José R ^a   Mazzi, Sonia ^a   Romo, Juan ^a   Zamar, Ruben H ^a  

^a NONE

Author keywords

Breakdown point; M estimates; Maxbias curve; Robust regression; Scale; Sensitivity

Indexed keywords

EID: 0032221153     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315515     Document Type: Article

References (16)

1. Berrendero, J.R., and Zamar, R.H. (1995). On the maxbias curve of residual admissible robust regression estimates. Working Paper 95-62, Universidad Carlos III de Madrid, Spain.
2. Croux, C. (1994). Efficient high-breakdown M-estimators of scale. Statist. Probab. Lett., 19, 371-379.
3. Donoho, D.L., and Huber, P.J. (1983). The notion of breakdown point. A Festchrift for Erich A. Lehmann (P. Bickel, K. Doksum, and J.L. Hodges Jr., eds.), Wadsworth, Belmont, Calif., 157-184.
4. Hampel, F.R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc., 69, 383-393.
5. He, X., and Simpson, D.G. (1993). Lower bounds for contamination bias: Globally minimax versus locally linear estimation. Ann. Statist., 21, 314-337.
6. Huber, P.J. (1964). Robust estimation of a location parameter. Ann. Math. Statist., 35, 73-101.
7. Huber, P.J. (1981). Robust Statistics. Wiley, New York.
8. Martin, R.D., and Zamar, R.H. (1989). Asymptotically min-max bias robust M-estimates of scale for positive random variables. J. Amer. Statist. Assoc., 17, 494-501.
9. Martin, R.D., Yohai, V.J., and Zamar, R.H. (1989). Min-max bias robust regression. Ann. Statist., 17, 1608-1630.
10. Rousseeuw, P.J., and Croux, C. (1994). The bias of k-step M-estimators. Statist. Probab. Lett., 20, 411-420.
11. Rousseeuw, P.J., and Leroy, A.M. (1987). Robust Regression and Outlier Detection. Wiley, New York.
12. Rousseeuw, P.J., and Yohai, V.J. (1984). Robust regression by means of S-estimators. Robust and Nonlinear Time Series Analysis (J. Franke, W. Härdie, and R.D. Martin, eds.), Lecture Notes in Statistics 26, Springer Verlag, New York, 256-272.
13. Rupport, D. (1992). Computing S-estimators for regression and multivariate location/dispersion. J. Comput. Graph. Statist., 1, 253-270.
14. Yohai, V.J. (1987). High breakdown point and high efficiency robust estimates for regression. Ann. Statist., 15, 642-656.
15. 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.
16. Yohai, V.J., and Zamar, R.H. (1993). A minimax bias property of the least α-quantile estimates. Ann. Statist., 20, 1875-1888.