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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 30, Issue 4


Bernstein estimator for unbounded copula densities

Taoufik Bouezmarni / El Ghouch / Abderrahim Taamouti
Published Online: 2013-12-10 | DOI: https://doi.org/10.1524/strm.2013.2003


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.

Keywords: Unbounded copula; nonparametric estimation; Bernstein density copula estimator; asymptotic properties; uniform strong consistency; relative convergence; boundary bias

About the article

Accepted: 2013-08-18

Received: 2013-01-29

Published Online: 2013-12-10

Published in Print: 2013-12-01

Citation Information: Statistics & Risk Modeling, Volume 30, Issue 4, Pages 343–360, ISSN (Online) 2196-7040, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2013.2003.

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