ESTIMATION OF THE SPECTRAL MEASURE FROM CONVEX COMBINATIONS OF REGULARLY VARYING RANDOM VECTORS

• 成果类型: Article
• 署名作者: Oesting, Marco; Wintenberger, Olivier
• 署名单位: University of Stuttgart; University of Stuttgart; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2387
• 发表日期: 2024
• 页码: 2529-2556
• 关键词: nonparametric-estimation; tail dependence; extreme; MULTIVARIATE; inference; maxima

摘要

The extremal dependence structure of a regularly varying random vector X is fully described by its limiting spectral measure. In this paper, we investigate how to recover characteristics of the measure, such as extremal coefficients, from the extremal behaviour of convex combinations of components of X. Our considerations result in a class of new estimators of moments of the corresponding combinations for the spectral vector. We show asymptotic normality by means of a functional limit theorem and, focusing on the estimation of extremal coefficients, we verify that the minimal asymptotic variance can be achieved by a plug-in estimator using subsampling bootstrap. We illustrate the benefits of our approach on simulated and real data.