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Testing independence based on Bernstein empirical copula and copula density.

Belalia, M. and Bouezmarni, T. and Lemyre, F.C. and Taamouti, A. (2017) 'Testing independence based on Bernstein empirical copula and copula density.', Journal of nonparametric statistics., 29 (2). pp. 346-380.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher 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:
Date accepted:25 October 2016
Date deposited:02 November 2016
Date of first online publication:23 March 2017
Date first made open access:23 March 2018

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