A New Test Procedure of Independence in Copula Models via χ²-Divergence

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 χ²-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.

Keywords:

• Asymptotic theory
• Dependence function
• Gumbel copula
• Multivariate rank statistics
• Pseudo-likelihood
• Semiparametric estimation

Mathematics Subject Classification:

• 62F03
• 62F10
• 62F12
• 62H12
• 62H15

Acknowledgment

The authors are grateful to the two referees for their useful suggestions and constructive criticisms on earlier drafts of this work.