Dependence properties and Bayesian inference for asymmetric multivariate copulas

Julyan Arbel 1 Marta Crispino 1 Stéphane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We study a broad class of asymmetric copulas introduced by Liebscher (2008) as a combination of multiple-usually symmetric-copulas. The main thrust of the paper is to provide new theoretical properties including exact tail dependence expressions and stability properties. A subclass of Liebscher copulas obtained by combining Fréchet copulas is studied in more details. We establish further dependence properties for copulas of this class and show that they are characterized by an arbitrary number of singular components. Furthermore, we introduce a novel iterative representation for general Liebscher copulas which de facto insures uniform margins, thus relaxing a constraint of Liebscher's original construction. Besides, we show that this iterative construction proves useful for inference by developing an Approximate Bayesian computation sampling scheme. This inferential procedure is demonstrated on simulated data.
Type de document :
Pré-publication, Document de travail
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Contributeur : Stephane Girard <>
Soumis le : vendredi 21 décembre 2018 - 17:19:08
Dernière modification le : vendredi 4 janvier 2019 - 17:00:10
Document(s) archivé(s) le : vendredi 22 mars 2019 - 17:56:02


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  • HAL Id : hal-01963975, version 1



Julyan Arbel, Marta Crispino, Stéphane Girard. Dependence properties and Bayesian inference for asymmetric multivariate copulas. 2018. 〈hal-01963975〉



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