Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application

Cécile Mercadier (1) , Paul Ressel (2)

1 PSPM - Probabilités, statistique, physique mathématique
2 KU - Katholishe Universität Eichstätt

The paper investigates the Hoeffding-Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transfered to the terms of the functional decomposition, and in addition to their individual variances, or to the superset combinations of those. The domain of integration in the resulting formulae is reduced in comparison with the already known expressions. When the function under study is the stable tail dependence function of a random vector, ranking these superset indices corresponds to cluster the components of the random vector with respect to their asymptotic dependence. Their Choquet representation is the main ingredient in deriving a sharp upper bound for the quantities involved in the tail dependograph, a graph in extreme value theory that summarizes asymptotic dependence.

Mots clés: Hoeffding--Sobol decomposition; Co-survival function; Spectral representation; Stable tail dependence function; Multivariate extreme value modelling

Domaines: Statistiques [math.ST]

Cécile Mercadier, Paul Ressel. Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application. Dependence Modeling, 2021, 9, pp.179-198. ⟨10.1515/demo-2021-0108⟩. ⟨hal-03200817v2⟩