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Zuo, Yijun; Cui, Hengjian; He, Xuming

On the Stahel-Donoho estimator and depth-weighted means of multivariate data. (English) Zbl 1105.62349

Ann. Stat. 32, No. 1, 167-188 (2004).
Summary: 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.

Cited in 1 Review
Cited in 45 Documents

MSC:

62H12 Estimation in multivariate analysis
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)

Keywords:

asymptotic normality; depth; breakdown point; efficiency; projection depth; \(L\)-estimator; robustness
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Full Text: DOI Euclid

References:

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