The influence function and maximum bias of Tukey's median

• 成果类型: Article
• 署名作者: Chen, ZQ; Tyler, DE
• 署名单位: William Paterson University New Jersey; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 1737-1759
• 关键词: multivariate location; M-ESTIMATORS; depth

摘要

Tukey's median is among one of the earliest known high breakdown point multivariate location statistics. Aside from its breakdown point, though, little else appears to be known about its robustness properties. In this paper we investigate other aspects of Tukey's median, and in particular we derive and study its influence function and its maximum contamination bias function. When judged by these other robustness criteria, Tukey's median again proves to be highly robust.