Comparaison Simultanée de $K\geq 2$ Copules Multivariées

We propose a test procedure to compare simultaneously K copulas, with K ≥ 2. The K observed populations can be paired. The test statistic is based on the differences between orthogonal projection coefficients associated to the density copulas, that we called copula coefficients. The procedure is data driven and we obtain a chi-square asymptotic distribution of the test statistic under the null. We illustrate our procedure via numerical studies and through two real datasets. Eventually, a clustering algorithm is deduced from the Ksample test and its performances are illustrated in a simulation experiment