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

• 成果类型: Article
• 署名作者: Zuo, YJ; Cui, HJ; He, XM
• 署名单位: Michigan State University; University of Illinois System; University of Illinois Urbana-Champaign; Beijing Normal University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2004
• 页码: 167-188
• 关键词: limit-theorems; location; regression; CONVERGENCE; statistics; BEHAVIOR; contours; scatter; tests

摘要

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.