Testing Independence Based on Bernstein Empirical Copula and Copula Density

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

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