On the weighted tests of independence based on Bernstein empirical copula

Abstract

In this article, we propose a flexible weighted test of independence based on Cramér-von Mises statistic of the Bernstein empirical copula process. We investigate the asymptotic properties of the new weighted test. A Monte Carlo study is conducted to measure the power performance of the new test under various dependence structures and also to compare the performance with some other alternative tests. The effects of the weights and the selection of optimal Bernstein polynomial degree are significantly influencing the power of the test according to the particular type of dependence. Finally, the procedure is also applied to a dataset on diabetes for illustrative purpose.

Keywords:

• Bernstein empirical copula
• Independence tests
• Monte Carlo simulation
• Power analysis
• Weighted Cramér-von Mises statistic

Mathematical Subject Classification:

• 62G10

Acknowledgments

We thank the anonymous referees for their helpful suggestions and comments which improved the presentation of the paper.