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Bernstein Estimator for Unbounded Density Copula

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  • Bouezmarni, Taoufik
  • El Ghouch, Anouar
  • Taamouti, Abderrahim

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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  • Bouezmarni, Taoufik & El Ghouch, Anouar & Taamouti, Abderrahim, 2011. "Bernstein Estimator for Unbounded Density Copula," LIDAM Discussion Papers ISBA 2011027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2011027
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    References listed on IDEAS

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    1. 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.
    2. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    3. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    4. 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, September.
    5. W. Gawronski & U. Stadtmüller, 1981. "Smoothing histograms by means of lattice-and continuous distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 28(1), pages 155-164, December.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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. Hernández-Maldonado, Victor Miguel & Erdely, Arturo & Díaz-Viera, Martín & Rios, Leonardo, 2024. "Fast procedure to compute empirical and Bernstein copulas," Applied Mathematics and Computation, Elsevier, vol. 477(C).

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