Estimation of extreme depth-based quantile regions

• 成果类型: Article
• 署名作者: He, Yi; Einmahl, John H. J.
• 署名单位: Tilburg University; Tilburg University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12163
• 发表日期: 2017
• 页码: 449-461
• 关键词: half-space depth; MULTIVARIATE

摘要

Consider the extreme quantile region induced by the half-space depth function HD of the form Q={xRd:HD(x,P)}, such that PQ=p for a given, very small p>0. Since this involves extrapolation outside the data cloud, this region can hardly be estimated through a fully non-parametric procedure. Using extreme value theory we construct a natural semiparametric estimator of this quantile region and prove a refined consistency result. A simulation study clearly demonstrates the good performance of our estimator. We use the procedure for risk management by applying it to stock market returns.