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            <title xml:lang="en">Non-parametric Clustering of Multivariate Populations with Arbitrary Sizes</title>
            <title xml:lang="fr">Classification Automatique de populations multivariées avec des tailles arbitraires via leur structure de dépendance</title>
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                <term xml:lang="en">Copula coefficients</term>
                <term xml:lang="en">data-driven</term>
                <term xml:lang="en">Legendre polynomials</term>
                <term xml:lang="en">nonparametric clustering</term>
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              <p>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.</p>
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