Dependence Properties of Multivariate Max-Stable Distributions

2012/10/31 by Papastathopoulos, Ioannis, Tawn, Jonathan A.
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1210.8268

Abstract

For an m-dimensional multivariate extreme value distribution there exist 2^m-1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we generalise the inequalities of Schlather and Tawn (2002) for the sets of extremal coefficients and construct bounds that higher order exponent measures need to satisfy to be consistent with lower order exponent measures. Subsequently we construct nonparametric estimators of the exponent measures which impose, through a likelihood-based procedure, the new dependence constraints and provide an improvement on the unconstrained estimators.

Related

• Max-min dependence coefficients for Multivariate Extreme Value Distributions
• Asymptotic properties of the maximum likelihood estimator for\n multivariate extreme value distributions
• Max-Stable Models for Multivariate Extremes
• Dependence of multivariate extremes
• Multivariate Extremes Over a Random Number of Observations