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October 1999 Asymptotics of reweighted estimators of multivariate location and scatter
Hendrik P. Lopuhaä
Ann. Statist. 27(5): 1638-1665 (October 1999). DOI: 10.1214/aos/1017939145


We investigate the asymptotic behavior of a weighted sample mean and covariance,where the weights are determined by the Mahalanobis distances with respect to initial robust estimators.We derive an explicit expansion for the weighted estimators. From this expansion it can be seen that reweighting does not improve the rate of convergence of the initial estimators.We also show that if one uses smooth $S$-estimators to determine the weights, the weighted estimators are asymptotically normal. Finally, we will compare the efficiency and local robustness of the reweighted $S$-estimators with two other improvements of $S$-estimators: $\tau$-estimators and constrained $M$-estimators.


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Hendrik P. Lopuhaä. "Asymptotics of reweighted estimators of multivariate location and scatter." Ann. Statist. 27 (5) 1638 - 1665, October 1999.


Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0957.62017
MathSciNet: MR2000M:62005
Digital Object Identifier: 10.1214/aos/1017939145

Primary: 62E20, 62F12, 62F35, 62H10, 62H12

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 5 • October 1999
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