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

On certain transformations of Archimedean copulas: Application to the non-parametric estimation... AbstractWe study the impact of certain transformations within theclass of Archimedean copulas. We give some admissibilityconditions for these transformations, and define some equivalenceclasses for both transformations and generators ofArchimedean copulas. We extend the r-fold composition ofthe diagonal section of a copula, from r ∈ N to r ∈ R. This extension,coupled with results on equivalence classes, gives usnew expressions of transformations and generators. Estimatorsderiving directly from these expressions are proposedand their convergence is investigated. We provide confidencebands for the estimated generators. Numerical illustrationsshow the empirical performance of these estimators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

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

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Publisher
de Gruyter
Copyright
©2013 Versita Sp. z o.o.
ISSN
2300-2298
eISSN
2300-2298
DOI
10.2478/demo-2013-0001
Publisher site
See Article on Publisher Site

Abstract

AbstractWe study the impact of certain transformations within theclass of Archimedean copulas. We give some admissibilityconditions for these transformations, and define some equivalenceclasses for both transformations and generators ofArchimedean copulas. We extend the r-fold composition ofthe diagonal section of a copula, from r ∈ N to r ∈ R. This extension,coupled with results on equivalence classes, gives usnew expressions of transformations and generators. Estimatorsderiving directly from these expressions are proposedand their convergence is investigated. We provide confidencebands for the estimated generators. Numerical illustrationsshow the empirical performance of these estimators.

Journal

Dependence Modelingde Gruyter

Published: Jan 1, 2013

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