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Nonparametric estimation of copulas and copula densities by orthogonal projections

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  • Ngounou Bakam, Yves I.
  • Pommeret, Denys

Abstract

A nonparametric copula density estimator based on Legendre orthogonal polynomials is proposed. A nonparametric copula estimator is then deduced by integration. Their asymptotic properties are reviewed. Both estimators are based on a sequence of moments that characterize the copulas and that we shall call the copula coefficients. A data-driven method is proposed to select the number of copula coefficients to use. An intensive simulation study shows the good performance of both copulas and copula densities estimators compared to a large panel of competitors. Two real datasets illustrate this approach.

Suggested Citation

  • Ngounou Bakam, Yves I. & Pommeret, Denys, 2025. "Nonparametric estimation of copulas and copula densities by orthogonal projections," Econometrics and Statistics, Elsevier, vol. 36(C), pages 90-118.
    • Handle: RePEc:eee:ecosta:v:36:y:2025:i:c:p:90-118
    DOI: 10.1016/j.ecosta.2023.04.002
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