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Asymptotic properties of the Bernstein density copula for dependent data

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  • BOUEZMARNI, Taoufik

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  • ROMBOUTS, Jeroen V.K.
  • TAAMOUTI, Abderrahim

Abstract

Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for α-mixing data using Bernstein polynomials. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality.

Suggested Citation

  • BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K. & TAAMOUTI, Abderrahim, 2008. "Asymptotic properties of the Bernstein density copula for dependent data," LIDAM Discussion Papers CORE 2008045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2008045
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    Cited by:

    1. Dietmar Pfeifer & Doreen Strassburger & Joerg Philipps, 2020. "Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulas," Papers 2010.15709, arXiv.org.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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