Maxbias curves of robust scale estimators based on subranges

Metrika

Volumn 53, Issue 2, 2001, Pages 101-122

  Croux, Christophe ^a   Haesbroeck, Gentiane ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Breakdown point; Maxbias curve; Robustness; Scale estimation

Indexed keywords

EID: 0035649212     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00003987     Document Type: Article

References (26)

1. Adrover JG (1998) Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution. The Annals of Statistics 26:2301-2320
2. Berrendero JR, Mazzi S, Romo J. Zamar RH (1998) On the explosion rate of maximum bias functions. Canadian Journal of Statistics 26:333-351
3. Berrendero JR, Romo J (1998) Stability under contamination of robust regression estimators based on differences of residuals. Journal of Statistical Planning and Inference 70:149-165
4. Berrendero JR, Zamar, RH (1999) Global robustness of location and dispersion estimates. Statistics and Probability Letters 44:63-72
5. Bickel PJ, Lehmann EL (1976) Descriptive statistics for nonparametric models. III. Dispersion. The Annals of Statisticsc 4:1139-1159
6. Butler RW, Davies PL, Jhun M (1993) Asymptotics for the minimum covariance determinant estimator. The Annals of Statistics 21:1385-1400
7. Croux C, Haesbroeck G (1999a) Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. Journal of Multivariate Analysis 71:161-190
8. Croux C, Haesbroeck G (1999b) Maxbias curves of robust scale estimators based on subranges. Technical Report. University of Liège: http://www.eaa.egss.ulg.ac.be/Haesbroeck
9. Croux C, Rousseeuw PJ (1992) A class of high-breakdown scale estimators based on subranges. Communications in Statistics-Theory and Methods 21:1935-1951
10. Croux C, Rousseeuw PJ, Van Bael A ( 1996) Positive breakdown regression by minimizing nested scale estimators. Journal of Statistical Planning and Inference 53:197-235
11. Grübel R (1988) The length of the shorth. The Annals of Statistics 16:619-628
12. Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics: The approach based on influence functions. Wiley, New York
13. He X, Simpson DG (1993) Lower bounds for contamination bias: Globally minimax versus locally linear estimation. The Annals of Statistics 21:314-337
14. Hössjer O, Rousseeuw PJ, Croux C (1996) Asymptotics of an estimator of a robust spread functional. Statistica Sinica 6:375-388
15. Huber PJ (1981) Robust statistics. Wiley, New York
16. Jurečová J, Sen PK (1996) Robust statistical procedures, asymptotics and interrelations. Wiley, New York
17. Martin RD, Yohai VJ, Zamar RH (1989) Min-max bias robust regression. The Annals of Statistics 17:1608-1630
18. Martin RD, Zamar RH (1989) Asymptotically min-max bias robust M-estimates of scale for positive random variables. Journal of the American Statistical Association 84:494-501
19. Martin RD, Zamar RH (1993) Bias robust estimation of scale. The Annals of Statistics 21:991-1017
20. Rousseeuw PJ (1985) Multivariate estimation with high breakdown point. In: Grossmann W, Pflug G, Vincze I, Wertz W (eds.) Mathematical Statistics and Applications (Vol. B). Reidel, Dordrecht, pp. 283-297
21. Rousseeuw PJ (1998) Maxbias curves. In: Kotz S, Read C, Banks D (eds.) Encyclopedia of Statistical Sciences Update Volume 3. Wiley, New York
22. Rousseeuw PJ, Croux C (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association 88:1273-1283
23. Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York
24. Rousseeuw PJ, Leroy AM (1988) A robust scale estimator based on the shortest half. Statistica Neerlandica 42:103-116
25. Yohai VJ, Maronna RA (1990) The maximum bias of robust covariances. Communications in Statistics Part A - Theory and Methods 19:3925-3933
26. Yohai VJ, Zamar RH (1993) A minimax-bias property of the least α-quantile estimates. The Annals of Statistics 4:1824-1842