Sampling from hierarchical Kendall copulas

Brechmann, Eike Christian

Journal de la société française de statistique, Tome 154 (2013) no. 1, pp. 192-209.

Les copules étant fréquemment utilisées pour modéliser la dépendance, il est crucial de disposer d’algorithmes efficaces permettant de générer des échantillons pseudo-aléatoires à partir de ces distributions. Dans le cas des copules de Kendall hiérarchiques, une stratégie d’échantillonnage descendante repose sur la simulation d’un vecteur aléatoire sachant qu’il prend ses valeurs dans un ensemble de niveau de la copule. Après avoir rappelé les solutions explicites dans le cas où la construction repose sur les copules Archimédiennes, cet article présente de nouveaux résultats pour la copule de Plackett et pour les copules Archimax contenant la classe des copules de valeurs extrêmes. En complément, de nouveaux algorithmes approchés de génération d’échantillons pseudo-aléatoires pour les copules de Kendall hiérarchiques sont proposés et évalués par le biais de simulations.

As copulas are frequently used to model dependence in statistical models, it is of central importance to be able to accurately and efficiently sample from them. In the case of hierarchical Kendall copulas, a top-down sampling strategy involves simulation of a random vector given that it lies in a particular level set. While explicit solutions are available when hierarchical Kendall copulas are built from Archimedean copulas, this paper presents new results for the Plackett copula and for Archimax copulas, which also include the class of extreme-value copulas. Additionally, new approximate sampling procedures for hierarchical Kendall copulas are proposed and evaluated in a simulation study.

Keywords: sampling copulas, hierarchical copulas, Kendall distribution function, copula level set, sample reordering
Mot clés : génération d’échantillons pseudo-aléatoires, copules hiérarchiques, fonction de distribution de Kendall, ensembles de niveau d’une copule

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