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BY 4.0 license Open Access Published by De Gruyter Open Access September 25, 2021

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

  • Cécile Mercadier EMAIL logo and Paul Ressel
From the journal Dependence Modeling

Abstract

The paper investigates the Hoeffding–Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transferred 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 clustering 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.

MSC 2010: 26A48; 26B99; 44A30; 62G32; 62H05

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Received: 2021-04-18
Accepted: 2021-08-26
Published Online: 2021-09-25

© 2021 Cécile Mercadier et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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