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Nonparametric estimation of copulas and copula densities by orthogonal projections

Abstract : In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then deduced. Its asymptotic properties are studied: we provide a large functional class for which this construction is optimal in the minimax and maxiset sense and we propose a method selection for the smoothing parameter. An intensive simulation study shows the very good performance of both copulas and copula densities estimators which we compare to a large panel of competitors. A real dataset in actuarial science illustrates this approach.
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Preprints, Working Papers, ...
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https://hal-amu.archives-ouvertes.fr/hal-03100036
Contributor : Yves Ismaël Ngounou Bakam Connect in order to contact the contributor
Submitted on : Wednesday, January 6, 2021 - 2:22:37 PM
Last modification on : Tuesday, October 19, 2021 - 10:49:38 PM

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  • HAL Id : hal-03100036, version 1
  • ARXIV : 2010.15351

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Yves I. Ngounou Bakam, Denys Pommeret. Nonparametric estimation of copulas and copula densities by orthogonal projections. 2021. ⟨hal-03100036⟩

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