In this paper, tests of symmetry for bivariate copulas are introduced and studied using empirical Bernstein copula. Three statistics are proposed and their asymptotic properties are established. Besides, a multiplier bootstrap Bernstein version is investigated for implementation purpose. Simulation study and real data application showed that the Bernstein tests outperform the tests based on the empirical copula.

翻译：本文采用伯恩斯坦(Bernstein copula)经验经验来介绍和研究双差相交合体的对称性测试,提出了三项统计数据,并确定了它们的无症状特性,此外,还调查了一个用于执行目的的倍增效应靴贝恩斯坦(Bernstein)版本。模拟研究和实际数据应用表明伯恩斯坦(Bernstein)测试优于基于经验性 Copula(Bernstein)的测试。