Non-parametric Clustering of Multivariate Populations with Arbitrary Sizes

We propose a clustering procedure to group K populations into subgroups with the same dependence structure. The method is adapted to paired population and can be used with panel data. It relies on the differences between orthogonal projection coefficients of the K density copulas estimated from the K populations. Each cluster is then constituted by populations having significantly similar dependence structures. A recent test statistic from Ngounou-Bakam and Pommeret (2022) is used to construct automatically such clusters. The procedure is data driven and depends on the asymptotic level of the test. We illustrate our clustering algorithm via numerical studies and through two real datasets: a panel of financial datasets and insurance dataset of losses and allocated loss adjustment expense.