Open Access
February 2004 On the Stahel-Donoho estimator and depth-weighted means of multivariate data
Yijun Zuo, Hengjian Cui, Xuming He
Ann. Statist. 32(1): 167-188 (February 2004). DOI: 10.1214/aos/1079120132


The depth of multivariate data can be used to construct weighted means as robust estimators of location. The use of projection depth leads to the Stahel-Donoho estimator as a special case. In contrast to maximal depth estimators, the depth-weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature. We also confirm through a finite-sample study that the Stahel-Donoho estimator achieves a desirable balance between robustness and efficiency at Gaussian models.


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Yijun Zuo. Hengjian Cui. Xuming He. "On the Stahel-Donoho estimator and depth-weighted means of multivariate data." Ann. Statist. 32 (1) 167 - 188, February 2004.


Published: February 2004
First available in Project Euclid: 12 March 2004

zbMATH: 1105.62349
MathSciNet: MR2051003
Digital Object Identifier: 10.1214/aos/1079120132

Primary: 62E20 , 62F12
Secondary: 62F35 , 62G35

Keywords: $L$-estimator , asymptotic normality , Breakdown point , depth , efficiency , projection depth , robustness

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 1 • February 2004
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