ESTIMATION OF EXTREME RISK REGIONS UNDER MULTIVARIATE REGULAR VARIATION

• 成果类型: Article
• 署名作者: Cai, Juan-Juan; Einmahl, John H. J.; De Haan, Laurens
• 署名单位: Tilburg University; Universidade de Lisboa; Tilburg University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS891
• 发表日期: 2011
• 页码: 1803-1826
• 关键词: nonparametric-estimation; density; index; rates; tail

摘要

When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form {z is an element of R-d : f (z) <= beta}, where f is the joint density and beta a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given a random sample of multivariate regularly varying random vectors. In a detailed simulation and comparison study, the good performance of the procedure is demonstrated. We also apply our estimator to financial data.