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Testing independence based on Bernstein empirical copula and copula density

Author

Listed:
  • M. Belalia
  • T. Bouezmarni
  • F. C. Lemyre
  • A. Taamouti

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.

Suggested Citation

  • M. Belalia & T. Bouezmarni & F. C. Lemyre & A. Taamouti, 2017. "Testing independence based on Bernstein empirical copula and copula density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 346-380, April.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:346-380
    DOI: 10.1080/10485252.2017.1303063
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    Citations

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    Cited by:

    1. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Lu Lu & Sujit Ghosh, 2023. "Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods," Mathematics, MDPI, vol. 11(20), pages 1-22, October.
    3. Hernández-Maldonado, Victor Miguel & Erdely, Arturo & Díaz-Viera, Martín & Rios, Leonardo, 2024. "Fast procedure to compute empirical and Bernstein copulas," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    4. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 266-281.
    5. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    6. Lingyue Zhang & Dawei Lu & Xiaoguang Wang, 2020. "Measuring and testing interdependence among random vectors based on Spearman’s $$\rho $$ ρ and Kendall’s $$\tau $$ τ," Computational Statistics, Springer, vol. 35(4), pages 1685-1713, December.

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