Testing Symmetry for Bivariate Copulas using Bernstein Polynomials

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.