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Dependence properties and Bayesian inference for asymmetric multivariate copulas

Julyan Arbel 1 Marta Crispino 1 Stéphane Girard 1
1 MISTIS [2016-2019] - Modelling and Inference of Complex and Structured Stochastic Systems [2016-2019]
Inria Grenoble - Rhône-Alpes, LJK [2016-2019] - Laboratoire Jean Kuntzmann [2016-2019], Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019]
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 comonotonic copulas is studied in more detail.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 and is compared to a likelihood-based approach in a setting where the latter is available.
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https://hal.archives-ouvertes.fr/hal-01963975
Contributor : Stephane Girard <>
Submitted on : Friday, June 28, 2019 - 1:56:45 PM
Last modification on : Thursday, August 6, 2020 - 3:16:56 AM

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Julyan Arbel, Marta Crispino, Stéphane Girard. Dependence properties and Bayesian inference for asymmetric multivariate copulas. Journal of Multivariate Analysis, Elsevier, 2019, 174, pp.104530:1-20. ⟨10.1016/j.jmva.2019.06.008⟩. ⟨hal-01963975v2⟩

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