On depth and deep points: A calculus

• 成果类型: Article
• 署名作者: Mizera, I
• 署名单位: University of Alberta; Comenius University Bratislava
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 1681-1736
• 关键词: regression depth; MULTIVARIATE; aggregation; CONVERGENCE; probability

摘要

For a general definition of depth in data analysis a differential-like calculus is constructed in which the location case (the framework of Tukey's median) plays a fundamental role similar to that of linear functions in the mathematical analysis. As an application, a lower bound for maximal regression depth is proved in the general multidimensional case-as conjectured by Rousseeuw and Hubert and others. This lower bound is demonstrated to have an impact on the breakdown point of the maximum depth estimator.