Concentration of the empirical level sets of Tukey's halfspace depth
成果类型：
Article
署名作者：
Brunel, Victor-Emmanuel
署名单位：
Massachusetts Institute of Technology (MIT)
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0850-0
发表日期：
2019
页码：
1165-1196
关键词：
摘要：
Tukey's halfspace depth has attracted much interest in data analysis, because it is a natural way of measuring the notion of depth relative to a cloud of points or, more generally, to a probability measure. Given an i.i.d. sample, we investigate the concentration of upper level sets of the Tukey depth relative to that sample around their population version. We show that under some mild assumptions on the underlying probability measure, concentration occurs at a parametric rate and we deduce moment inequalities at that same rate. In a computational prospective, we study the concentration of a discretized version of the empirical upper level sets.
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