Testing Independence Based on Bernstein Empirical Copula and Copula Density

Belalia, M.; Bouezmarni, T.; Lemyre, F.C.; Taamouti, A.

doi:10.1080/10485252.2017.1303063

Testing Independence Based on Bernstein Empirical Copula and Copula Density

Belalia, M.; Bouezmarni, T.; Lemyre, F.C.; Taamouti, A.

Authors

M. Belalia

T. Bouezmarni

F.C. Lemyre

Professor Abderrahim Taamouti abderrahim.taamouti@durham.ac.uk
Visiting Fellow

Abstract

In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function.

Citation

Belalia, M., Bouezmarni, T., Lemyre, F., & Taamouti, A. (2017). Testing Independence Based on Bernstein Empirical Copula and Copula Density. Journal of Nonparametric Statistics, 29(2), 346-380. https://doi.org/10.1080/10485252.2017.1303063

Journal Article Type	Article
Acceptance Date	Oct 25, 2016
Online Publication Date	Mar 23, 2017
Publication Date	Apr 3, 2017
Deposit Date	Oct 31, 2016
Publicly Available Date	Mar 23, 2018
Journal	Journal of Nonparametric Statistics
Print ISSN	1048-5252
Electronic ISSN	1029-0311
Publisher	Taylor and Francis Group
Peer Reviewed	Peer Reviewed
Volume	29
Issue	2
Pages	346-380
DOI	https://doi.org/10.1080/10485252.2017.1303063
Public URL	https://durham-repository.worktribe.com/output/1394613

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Copyright Statement
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Nonparametric Statistics on 23/03/2017, available online at: http://www.tandfonline.com/10.1080/10485252.2017.1303063.