Characterizing extremal dependence on a hyperplane

• 成果类型: Article
• 署名作者: Wan, P.
• 署名单位: Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag015
• 发表日期: 2026
• 页码: asag015
• 关键词: extremal dependence; H & uuml; sler-Reiss model; Multivariate Extremes; Principal Component Analysis

摘要

In this paper, we characterize the extremal dependence of $ d $ asymptotically dependent variables using a class of random vectors on the $ (d-1) $-dimensional hyperplane perpendicular to the diagonal vector $ \mathbf{1}=(1,\ldots,1) $. This translates analyses of multivariate extremes to analyses on a linear vector space, opening up possibilities for applying existing statistical techniques based on linear operations. As an example, we demonstrate how to obtain lower-dimensional approximations of tail dependence through principal component analysis. Additionally, we show that the widely used H & uuml;sler-Reiss family is characterized by a Gaussian family residing on the hyperplane.