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

Salim Bouzebda (1) , Amor Keziou (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LMR - Laboratoire de Mathématiques de Reims

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 null and alternative hypothesis, with simple and standard limit distributions both when the parameter is an interior point or not.

Mots clés: Semiparametric estimation; Dependence function; Gumbel copula; pseudo-likelihood; Asymptotic theory; Multivariate rank statistic; Semiparametric estimation.

Domaines: Théorie [stat.TH]

Salim Bouzebda, Amor Keziou. A new test procedure of independence in copula models via chi-square-divergence. 2008. ⟨hal-00262077v1⟩