Estimating copula densities through wavelets

Christian Genest (1) , Esterina Masiello (2) , Karine Tribouley (2, 3)

1 Département de mathématiques et de statistique
2 MODAL'X - Modélisation aléatoire de Paris X
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Wavelet analysis is used to construct a rank-based estimator of a copula density. The procedure, which can be easily implemented with ready-to-use wavelet packages, is based on an algorithm that handles boundary effects automatically. The resulting estimator provides a nonparametric benchmark for the selection of a parametric copula family. From a theoretical point of view, the estimation procedure is shown to be optimal in the minimax sense on a large functional class of regular copula densities. The approach is illustrated with actuarial and financial data.

Mots clés: Wavelets; Copulas; Nonparametric Estimation; Ranks; Wavelets.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christian Genest, Esterina Masiello, Karine Tribouley. Estimating copula densities through wavelets. Insurance: Mathematics and Economics, 2009, 44 (2), pp.170-181. ⟨10.1016/j.insmatheco.2008.07.006⟩. ⟨hal-00257425v2⟩