Robust M-estimators of scale: Minimax bias versus maximal variance

Canadian Journal of Statistics

Volumn 27, Issue 1, 1999, Pages 81-96

  Collins, John R ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Asymptotic efficiency; Asymptotic variance; Minimax asymptotic bias; Robust estimation; Scale parameter

Indexed keywords

EID: 0033464228     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315492     Document Type: Article

References (12)

1. Collins, J.R. (1991). Maximal asymptotic biases and variances of symmetrized interquantile ranges under asymmetric contamination. Statistics 22, 379-402.
2. Hampel, F.R., Rousseeuw, P.J., and Ronchetti, E. (1981). The change-of-variance curve and optimal re-descending M-estimators. J. Amer. Statist. Assoc., 76, 643-648.
3. 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.
4. He, X., and Simpson, D.G. (1993). Lower bounds for contamination bias: globally minimax versus locally linear estimation. Ann. Statist., 21, 314-337.
5. Huber, P.J. (1964). Robust estimation of a location parameter. Ann. Math. Statist., 35, 73-101.
6. Huber, P.J. (1981). Robust Statistics. Wiley, New York.
7. 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., 84, 494-501.
8. Martin, R.D., and Zamar, R.H. (1993a). Efficiency-constrained bias-robust estimation of location. Ann. Statist., 21, 338-354.
9. Martin, R.D., and Zamar, R.H. (1993b). Bias robust estimation of scale. Ann. Statist., 21, 991-1017.
10. Rousseeuw, P.J. (1981). A new infinitesimal approach to robust estimation. Z. Wahrsch. Verw. Geb., 56, 127-132.
11. Rousseeuw, P.J., and Croux, C. (1993). Alternatives to the median absolute deviation. J. Amer. Statist. Assoc., 88, 1273-1286.
12. Rousseeuw, P.J., and Croux, C. (1994). The bias of k-step 2M-estimators. Statist. Probab. Lett., 20, 411-420.