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A mixture model for multivariate extremes
Author(s) -
Boldi M.O.,
Davison A. C.
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00585.x
Subject(s) - markov chain monte carlo , frequentist inference , univariate , parametric model , multivariate statistics , mathematics , dirichlet distribution , parametric statistics , moment (physics) , inference , dirichlet process , statistical physics , bayesian probability , reversible jump markov chain monte carlo , bayesian inference , statistics , computer science , artificial intelligence , physics , mathematical analysis , classical mechanics , boundary value problem
Summary. 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.