Convergence of depth contours for multivariate datasets

• 成果类型: Article
• 署名作者: He, XM; Wang, G
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; DePaul University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 495-504
• 关键词: location; estimators; dispersion

摘要

Contours of depth often provide a good geometrical understanding of the structure of a multivariate dataset. They are also useful in robust statistics in connection with generalized medians and data ordering. If the data constitute a random sample from a spherical or elliptic distribution, the depth contours are generally required to converge to spherical or elliptical shapes. We consider contour constructions based on a notion of data depth and prove a uniform contour convergence theorem under verifiable conditions on the depth measure. Applications to several existing depth measures discussed in the literature are also considered.