Asymptotic properties of the Bernstein density copula for dependent data

Bouezmarni, Taoufik;Rombouts, Jeroen;Taamouti, Abderrahim
(2008) , 12 pages

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Authors
  • Bouezmarni, TaoufikUniversité de Montréal, Canada
    Author
  • Rombouts, JeroenHEC Montréal, CIRANO, CIRPEE, Canada
    Author
  • Taamouti, AbderrahimUniversidad Carlos III de Madrid, Spain
    Author
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 á-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.
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Bouezmarni, T., Rombouts, J., & Taamouti, A. (2008). Asymptotic properties of the Bernstein density copula for dependent data (CORE Discussion papers 2008/45). https://hdl.handle.net/2078.5/249981