B1742
Title: K-sample test of copulas
Authors: Denys Pommeret - ISFA (Lyon 1) & I2M (France) [presenting]
Abstract: Copulas are still extensively studied and used to model the dependence of multivariate observations. Many applications can be found in the world of actuarial science by making it possible to detect mutualizable risks and not mutualizable; but also to build a well-diversified portfolio. We propose an equality test of $K$ copulas simultaneously, when $K$ populations are observed. We want to test the following null hypothesis $C_1=C_2=...=C_K$, from $K$ iid samples, possibly paired. We obtain the exact asymptotic null distribution of the test statistic and we prove the convergence of the test. The idea of the test is to transform the observations to uniform laws, then to use the decomposition of the density of the copula on an orthogonal Legendre polynomials basis. Returning to the copula function we obtain what is called copula coefficients which characterize each copula. The test then amounts to simultaneously comparing these coefficients. We apply this method to the ``Society of Actuaries Group Medical Insurance Large Claims Database'', in particular, we suggest a clustering algorithm to classify populations with similar dependence structures.
