General notions of statistical depth function

• 成果类型: Article
• 署名作者: Zuo, YJ; Serfling, R
• 署名单位: Arizona State University; Arizona State University-Tempe; University of Texas System; University of Texas Dallas
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016218226
• 发表日期: 2000
• 页码: 461-482
• 关键词: half-space depth; MULTIVARIATE-ANALYSIS; regression depth; breakdown point; location depth; distributions; aggregation; inference

摘要

Statistical depth Functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deepest point, and vanishing at infinity. This provides a more systematic basis for selection of a depth function. In particular, from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors.