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Preprints, Working Papers, ... Year : 2021

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.

Dates and versions

hal-03100036 , version 1 (06-01-2021)

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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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