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

Elena Di Bernardino
  • Conservatoire National des Arts et Métiers, Département IMATH, EA4629, 292 rue Saint Martin, 75011, Paris, France
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/ Didier Rullière
  • Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, EA2429, 50 avenue Tony Garnier, 69366 Lyon, France
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Published Online: 2013-10-21 | DOI: https://doi.org/10.2478/demo-2013-0001


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.

Keywords: Transformations of Archimedean copulas; self-nested diagonal; non-parametric estimation; tail dependence

MSC: 62H12; 62E17; 62G05; 62G20

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About the article

Received: 2013-06-13

Accepted: 2013-10-08

Published Online: 2013-10-21

Citation Information: Dependence Modeling, Volume 1, Pages 1–36, ISSN (Online) 2300-2298, DOI: https://doi.org/10.2478/demo-2013-0001.

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