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Scientific article
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A mixture model for multivariate extremes

Publication date2007
Abstract

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.

Keywords
  • Adequacy
  • Air pollution data
  • Dirichlet distribution
  • EM algorithm
  • Multivariate extreme values
  • Oceanographic data
  • Reversible jump Markov chain Monte Carlo simulation
  • Spectral distribution
Citation (ISO format)
BOLDI, Marc-Olivier, DAVISON, Anthony. A mixture model for multivariate extremes. In: Journal of the Royal Statistical Society. Series B, Statistical methodology, 2007, vol. 69, n° 2, p. 217–229.
Main files (1)
Article (Accepted version)
accessLevelPrivate
Identifiers
  • PID : unige:79895
ISSN of the journal1369-7412
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