A new test procedure of independence in copula models via   chi-square-divergence
  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. 
Salim Bouzebda (LSTA), Amor Keziou (LM-Reims)