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Bernstein estimator for unbounded copula densities

Bouezmarni, T.; El Gouch, A.; Taamouti, A.

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Authors

T. Bouezmarni

A. El Gouch



Abstract

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.

Citation

Bouezmarni, T., El Gouch, A., & Taamouti, A. (2013). Bernstein estimator for unbounded copula densities. Statistics & Risk Modeling, 30(4), 343-360. https://doi.org/10.1524/strm.2013.2003

Journal Article Type Article
Publication Date Dec 10, 2013
Deposit Date Aug 28, 2014
Publicly Available Date Mar 29, 2024
Journal Statistics and Risk Modeling
Print ISSN 2193-1402
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 30
Issue 4
Pages 343-360
DOI https://doi.org/10.1524/strm.2013.2003
Keywords Unbounded copula, Nonparametric estimation, Bernstein density copula estimator, Asymptotic properties, Uniform strong consistency, Relative convergence, Boundary bias.
Public URL https://durham-repository.worktribe.com/output/1454953

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Copyright Statement
The final publication is available at www.degruyter.com.




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