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Asymptotic properties of the Bernstein density copula for dependent data

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Author Info
BOUEZMARNI, Taoufik (---)
ROMBOUTS, Jeroen V.K.
TAAMOUTI, Abderrahim

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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 a-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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2008045.

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Date of creation: 01 Jul 2008
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Handle: RePEc:cor:louvco:2008045

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Related research
Keywords: nonparametric estimation; copula; Bernstein polynomial; a-mixing; asymptotic properties; boundary bias;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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References listed on IDEAS
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  1. 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. [Downloadable!] (restricted)
  2. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2002. "Efficient Estimation of Semiparametric Multivariate Copula Models," Working Papers 0420, Department of Economics, Vanderbilt University, revised Sep 2004. [Downloadable!]
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  3. 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(03), pages 535-562, June. [Downloadable!]
  4. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February. [Downloadable!] (restricted)
  5. Axel Tenbusch, 1997. "Nonparametric curve estimation with bernstein estimates," Metrika, Springer, vol. 45(1), pages 1-30, January. [Downloadable!] (restricted)
  6. Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(2), pages 253-287, 03. [Downloadable!] (restricted)
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