Testing independence based on Bernstein empirical copula and copula density. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: Belalia, M.; Bouezmarni, T.; Lemyre, F. C.; Taamouti, A.
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 2(2017)
• Page Start: 346
• Page End: 380
• Publication Date: 2017-04-03
• Subjects: Bernstein empirical copula -- copula density -- Cramér–von Mises statistic -- Kullback–Leibler divergence-type -- independence test; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2017.1303063
• Languages: English
• ISSNs: 1048-5252

Abstract

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.