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Bernstein estimator for unbounded copula densities.

Bouezmarni, T. and El Gouch, A. and Taamouti, A. (2013) 'Bernstein estimator for unbounded copula densities.', Statistics & risk modeling., 30 (4). pp. 343-360.

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.

Item Type:Article
Keywords:Unbounded copula, Nonparametric estimation, Bernstein density copula estimator, Asymptotic properties, Uniform strong consistency, Relative convergence, Boundary bias.
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1524/strm.2013.2003
Publisher statement:The final publication is available at www.degruyter.com.
Record Created:07 Nov 2014 12:35
Last Modified:14 Dec 2014 00:30

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