Decompositions of dependence for high-dimensional extremes

• 成果类型: Article
• 署名作者: Cooley, D.; Thibaud, E.
• 署名单位: Colorado State University System; Colorado State University Fort Collins; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz028
• 发表日期: 2019
• 页码: 587604
• 关键词: multivariate; INDEPENDENCE; inference

摘要

We propose two decompositions that help to summarize and describe high-dimensional tail dependence within the framework of regular variation. We use a transformation to define a vector space on the positive orthant and show that transformed-linear operations applied to regularly-varying random vectors preserve regular variation. We summarize tail dependence via a matrix of pairwise tail dependence metrics that is positive semidefinite; eigendecomposition allows one to interpret tail dependence in terms of the resulting eigenbasis. This matrix is completely positive, and one can easily construct regularly-varying random vectors that share the same pairwise tail dependencies. We illustrate our methods with Swiss rainfall and financial returns data.