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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.

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  • 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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    References listed on IDEAS

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    1. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    2. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    3. Bruce M. Brown & Song Xi Chen, 1999. "Beta‐Bernstein Smoothing for Regression Curves with Compact Support," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 47-59, March.
    4. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    5. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    6. Axel Tenbusch, 1997. "Nonparametric curve estimation with bernstein estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 1-30, January.
    7. Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, March.
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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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    More about this item

    Keywords

    nonparametric estimation; copula; Bernstein polynomial; α-mixing; asymptotic properties; boundary bias;
    All these keywords.

    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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