Testing Symmetry for Bivariate Copulas using Bernstein Polynomials

TL;DR

This paper introduces new symmetry tests for bivariate copulas using Bernstein polynomials, demonstrating their superior performance through simulations and real data applications.

Contribution

It develops three new symmetry test statistics based on Bernstein copulas and establishes their asymptotic properties, with a bootstrap implementation for practical use.

Findings

Bernstein tests outperform empirical copula-based tests in simulations

Tests yield consistent conclusions across various real data scenarios

Bootstrap Bernstein method enhances test implementation

Abstract

In this work, tests of symmetry for bivariate copulas are introduced and studied using empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a multiplier bootstrap Bernstein version is investigated for implementation purpose. The simulation study demonstrated the superior performance of the Bernstein tests compared to tests based on empirical copulas. Furthermore, in real data applications, these tests consistently yielded similar conclusions across a diverse range of scenarios.