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Bernstein estimator for unbounded density copula

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  • Taoufik Bouezmarni
  • Anouar El Ghouch

    ()

  • Abderrahim Taamouti

    ()

Abstract

We study the asymptotic properties of the Bernstein estimator for unbounded density copula functions. We show that the estimator converges to infinity at the corner. We establish its relative convergence when the copula is unbounded and we provide the uniform strong consistency of the estimator on every compact in the interior region. We also check the finite simple performance of the estimator via an extensive simulation study and we compare it with other well known nonparametric methods. Finally, we consider an empirical application where the asymmetric dependence between international equity markets (US, Canada, UK, and France) is re-examined.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1143.

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Date of creation: Oct 2011
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Handle: RePEc:cte:werepe:we1143

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Keywords: Unbounded copula; Nonparametric estimation; Bernstein polynomial; Asymptotic properties; Uniform strong consistency; Relative convergence; Boundary bias;

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  1. Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393.
  2. W. Gawronski & U. Stadtmüller, 1981. "Smoothing histograms by means of lattice-and continuous distributions," Metrika, Springer, vol. 28(1), pages 155-164, December.
  3. Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, 03.
  4. 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.
  5. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
  6. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
  7. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  8. Axel Tenbusch, 1997. "Nonparametric curve estimation with bernstein estimates," Metrika, Springer, vol. 45(1), pages 1-30, January.
  9. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
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