X-vine models for multivariate extremes

• 成果类型: Article
• 署名作者: Kiriliouk, Anna; Lee, Jeongjin; Segers, Johan
• 署名单位: University of Namur; Universite Catholique Louvain
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae105
• 发表日期: 2025
• 页码: 579-602
• 关键词: nonparametric-estimation; high dimensions; dependence; copulas; INDEPENDENCE; estimator; selection

摘要

Regular vine sequences permit the organization of variables in a random vector along a sequence of trees. Vine-based dependence models have become greatly popular as a way to combine arbitrary bivariate copulas into higher-dimensional ones, offering flexibility, parsimony, and tractability. In this project, we use regular vine sequences to decompose and construct the exponent measure density of a multivariate extreme value distribution, or, equivalently, the tail copula density. Although these densities pose theoretical challenges due to their infinite mass, their homogeneity property offers simplifications. The theory sheds new light on existing parametric families and facilitates the construction of new ones, called X-vines. Computations proceed via recursive formulas in terms of bivariate model components. We develop simulation algorithms for X-vine multivariate Pareto distributions as well as methods for parameter estimation and model selection on the basis of threshold exceedances. The methods are illustrated by Monte Carlo experiments and a case study on US flight delay data.