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Bernstein estimator for unbounded density copula

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  • Bouezmarni, Taoufik
  • El Ghouch, Anouar

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, 2011. "Bernstein estimator for unbounded density copula," UC3M Working papers. Economics we1143, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we1143
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    7. 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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    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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    Unbounded copula;

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