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

• Autorzy: Elena Di Bernardino , Didier Rullière
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 62H12: Estimation
• 62G20: Asymptotic properties
• 62G05: Estimation
• 62E17: Approximations to distributions (nonasymptotic)

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2013
• Tom: 1
• Strony: 1-36

Daty

otrzymano

2013-06-13

zaakceptowano

2013-10-08

online

2013-10-21

Twórcy

autor

Elena Di Bernardino

• Conservatoire National des Arts et Métiers, Département IMATH,
  EA4629, 292 rue Saint Martin, 75011, Paris, France

autor

Didier Rullière

• Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF,
  EA2429, 50 avenue Tony Garnier, 69366 Lyon, France

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Identyfikatory

DOI

10.2478/demo-2013-0001