A new test procedure of independence in copula models via chi-square-divergence

TL;DR

This paper proposes a novel chi-square-divergence based test for independence in parametric copula models with unknown marginals, analyzing its asymptotic properties under various conditions.

Contribution

It introduces a new test procedure leveraging chi-square-divergence dual representation, with comprehensive asymptotic analysis for different parameter scenarios.

Findings

Test statistic has standard limit distribution under null hypothesis.

Method effectively detects dependence in copula models.

Asymptotic properties are well-characterized for various parameter settings.

Abstract

We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $\chi^2$-divergence on signed finite measures. The asymptotic properties of the proposed estimate and the test statistic are studied under the null and alternative hypotheses, with simple and standard limit distributions both when the parameter is an interior point or not.