A sum characterization of hidden regular variation with likelihood inference via expectation-maximization

• 成果类型: Article
• 署名作者: Weller, Grant B.; Cooley, Daniel
• 署名单位: Carnegie Mellon University; Colorado State University System; Colorado State University Fort Collins
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast046
• 发表日期: 2014
• 页码: 1736
• 关键词: multivariate extreme values; em algorithm; nitrogen-dioxide; tail dependence; sulfur-dioxide; INDEPENDENCE; statistics

摘要

A fundamental deficiency of classical multivariate extreme value theory is the inability to distinguish between asymptotic independence and exact independence. In this work, we examine multivariate threshold modelling in the framework of regular variation on cones. Tail dependence is described by a limiting measure, which in some cases is degenerate on joint tail regions despite strong subasymptotic dependence in such regions. Hidden regular variation, a higher-order tail decay on these regions, offers a refinement of the classical theory. We develop a representation of random vectors possessing hidden regular variation as the sum of independent regular varying components. The representation is shown to be asymptotically valid via a multivariate tail equivalence result. We develop a likelihood-based estimation procedure from this representation via a Monte Carlo expectation-maximization algorithm which has been modified for tail estimation. The method is demonstrated on simulated data and applied to air pollution measurements.