A mixture model for multivariate extremes

• 成果类型: Article
• 署名作者: Boldi, M. -O.; Davison, A. C.
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2007.00585.x
• 发表日期: 2007
• 页码: 217-229
• 关键词: convergence assessment; maximum-likelihood; dependence

摘要

The spectral density function plays a key role in fitting the tail of multivariate extre-mal data and so in estimating probabilities of rare events. This function satisfies moment con-straints but unlike the univariate extreme value distributions has no simple parametric form. Parameterized subfamilies of spectral densities have been suggested for use in applications, and non-parametric estimation procedures have been proposed, but semiparametric models for multivariate extremes have hitherto received little attention. We show that mixtures of Dirichlet distributions satisfying the moment constraints are weakly dense in the class of all non-parametric spectral densities, and discuss frequentist and Bayesian inference in this class based on the EM algorithm and reversible jump Markov chain Monte Carlo simulation. We illustrate the ideas using simulated and real data.