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Bernstein estimator for unbounded copula densities

Listed author(s):
  • Bouezmarni Taoufik

    (1 Université de Sherbrooke)

  • Ghouch El

    (2Université Catholique de Louvain)

  • Taamouti Abderrahim

    ()

    (3Universidad Carlos III de Madrid)

Copulas are widely used for modeling the dependence structure of multivariate data. Many methods for estimating the copula density functions are investigated. In this paper, we study the asymptotic properties of the Bernstein estimator for unbounded copula density functions. We show that the estimator converges to infinity at the corner and we establish its relative convergence when the copula density is unbounded. Also, we provide the uniform strong consistency of the estimator on every compact in the interior region. We investigate the finite sample performance of the estimator via an extensive simulation study and we compare the Bernstein copula density estimator with other nonparametric methods. Finally, we consider an empirical application where the asymmetric dependence between international equity markets (US, Canada, UK, and France) is examined.

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Article provided by De Gruyter in its journal Statistics & Risk Modeling.

Volume (Year): 30 (2013)
Issue (Month): 4 (December)
Pages: 343-360

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Handle: RePEc:bpj:strimo:v:30:y:2013:i:4:p:343-360:n:3
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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. Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 233-253, December.
  3. 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.
  4. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
  5. 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.
  6. Bruce M. Brown, 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.
  7. 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.
  8. 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.
  9. 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.
  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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