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

Salim Bouzebda (1) , Amor Keziou (1, 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 the null and alternative hypotheses, with simple and standard limit distributions both when the parameter is an interior point or not.

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

Domaines: Théorie [stat.TH]

Salim Bouzebda, Amor Keziou. A new test procedure of independence in copula models via chi-square-divergence. Communications in Statistics - Theory and Methods, 2010. ⟨hal-00262077v2⟩