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

Elena Di Bernardino ; Didier Rullière

Dependence Modeling, Tome 1 (2013), p. 1-36 / Harvested from The Polish Digital Mathematics Library

Résumé

We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations 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.

Détail

Publié le : 2013-01-01

Zbl 1287.62005

EUDML-ID : urn:eudml:doc:267249

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