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

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  • Mercadier Cécile

    (Université de Lyon, Université Claude Bernard Lyon 1, Institut Camille Jordan, UMR CNRS 5208, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France)

  • Ressel Paul

    (Kath. Universität Eichstätt-Ingolstadt, Ostenstraße 26-28, 85072 Eichstätt, Germany)

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.

Suggested Citation

  • Mercadier Cécile & Ressel Paul, 2021. "Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application," Dependence Modeling, De Gruyter, vol. 9(1), pages 179-198, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:179-198:n:5
    DOI: 10.1515/demo-2021-0108
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    References listed on IDEAS

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