Zonoid trimming for multivariate distributions

• 成果类型: Article
• 署名作者: Koshevoy, G; Mosler, K
• 署名单位: Russian Academy of Sciences; Central Economics & Mathematics Institute RAS; University of Cologne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1998-2017
• 关键词: data depth; quantiles

摘要

A family of trimmed regions is introduced for a probability distribution in Euclidean d-space. The regions decrease with their parameter Lu, from the closed convex hull of support (at alpha = 0) to the expectation vector (at alpha = 1). The family determines the underlying distribution uniquely. For every cu the region is affine equivariant and continuous with respect to weak convergence of distributions. The behavior under mixture and dilation is studied. A new concept of data depth is introduced and investigated. Finally, a trimming transform is constructed that injectively maps a given distribution to a distribution having a unique median.