We develop a test of equality between two dependence structures estimated through empirical copulas. We provide inference for independent or paired samples. The multiplier central limit theorem is used for calculating p-values of the Cramér-von Mises test statistic. Finite sample properties are assessed with Monte Carlo experiments. We apply the testing procedure on empirical examples in finance, psychology, insurance and medicine.

Keywords : Copula, Cramér-von Mises statistic, empirical process, pseudo-observations, multiplier central limit theorem, p-value.

JEL : C12, C14, C15.

MSC 2000 : Primary 60F05; Secondary 62E20.