On the distortions of Archimedean copulas: Application to the non-parametric estimation of their generators

Elena Di Bernardino (1) , Didier Rullière (2)

1 CEDRIC - Centre d'études et de recherche en informatique et communications
2 SAF - Laboratoire de Sciences Actuarielle et Financière

We study the impact of some distortions for Archimedean copulas. We give some admissibility conditions for these distortions, and define some equivalence classes for both distortions and generators of Archimedean copulas. We investigate some impacts of the distortions on the tails of the distorted copula. We extend the r-fold composition of the diagonal section of a copula, from r in N to r in R. This extension, coupled with results on equivalence classes, gives us new expressions of distortions and generators. Estimators deriving directly from these expressions are proposed and their convergence is investigated. We provide confidence bands for the estimated generators. Numerical illustrations show the empirical performance of these estimators.

Mots clés: Distortions; Archimedean copula; auto-nested copula; non-parametric estimation; tail dependence

Domaines: Probabilités [math.PR]; Méthodologie [stat.ME]; Economies et finances

Elena Di Bernardino, Didier Rullière. On the distortions of Archimedean copulas: Application to the non-parametric estimation of their generators. 2013. ⟨hal-00834000v1⟩