On Truncation Invariant Copulas and their Estimation

Abstract

The paper deals with the family of irreducible left truncation invariant bivariate copulas, which admit a nontrivial lower tail dependence function. Such copulas, similarly as the Archimedean ones, are characterized by a functional parameter, a generator being an increasing convex function.We provide a nonparametric, piece-wise linear estimator of such generators.