The Annals of Statistics

On the Stahel-Donoho estimator and depth-weighted means of multivariate data

Yijun Zuo, Hengjian Cui, and Xuming He

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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.

Article information

Ann. Statist., Volume 32, Number 1 (2004), 167-188.

First available in Project Euclid: 12 March 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory 62F12: Asymptotic properties of estimators
Secondary: 62G35: Robustness 62F35: Robustness and adaptive procedures

Asymptotic normality depth breakdown point efficiency projection depth $L$-estimator robustness


Zuo, Yijun; Cui, Hengjian; He, Xuming. On the Stahel-Donoho estimator and depth-weighted means of multivariate data. Ann. Statist. 32 (2004), no. 1, 167--188. doi:10.1214/aos/1079120132.

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