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

Elena Di Bernardino; Didier Rullière

Dependence Modeling (2013)

  • Volume: 1, page 1-36
  • ISSN: 2300-2298

Abstract

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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.

How to cite

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Elena Di Bernardino, and Didier Rullière. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators." Dependence Modeling 1 (2013): 1-36. <http://eudml.org/doc/267249>.

@article{ElenaDiBernardino2013,
abstract = {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.},
author = {Elena Di Bernardino, Didier Rullière},
journal = {Dependence Modeling},
keywords = {Transformations of Archimedean copulas; self-nested diagonal; non-parametric estimation; tail dependence; estimation},
language = {eng},
pages = {1-36},
title = {On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators},
url = {http://eudml.org/doc/267249},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Elena Di Bernardino
AU - Didier Rullière
TI - On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators
JO - Dependence Modeling
PY - 2013
VL - 1
SP - 1
EP - 36
AB - 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.
LA - eng
KW - Transformations of Archimedean copulas; self-nested diagonal; non-parametric estimation; tail dependence; estimation
UR - http://eudml.org/doc/267249
ER -

References

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