Séminaire Statistique
organisé par l'équipe Statistique
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Yves Ngounou Bakam
Advancing Copula Methods: Nonparametric Estimation, Smooth Testing, and Data-Driven Clustering
14 mars 2025 - 11:00Salle de séminaires IRMA
Copulas, introduced in the 1950’s and rediscovered in recent years, are powerful tools for modeling dependence structures between multidimensional variables. These tools are particularly valuable in fields like finance, insurance, economics, and biology, where understanding the relationships between variables is critical. Despite their generality, copulas can present significant challenges, particularly when estimating dependence structures in complex datasets, especially when dealing with data from different sources, scales, and shapes. This work addresses three core challenges in copula modeling: estimation, testing, and clustering. We first propose a nonparametric copula density estimator based on Legendre orthogonal polynomials. A nonparametric copula estimator is then deduced by integration. Both estimates are based on a set of moments that define the copulas, and we’ll call them the copula coefficients. Flexible modeling is possible even when copula densities may not exist due to the complete characterization of these coefficients. A data-driven method is introduced to select the optimal number of copula coefficients to use, and extensive simulations show the superior performance of our approach compared to existing methods. Next, we propose a smooth test for comparing K ≥ 2, copulas simultaneously, based on differences in their copula coefficients. The procedure involves a two-step data-driven procedure. In the first step, the most significantly different coefficients are selected for all pairs of populations and the subsequent step utilizes these coefficients to identify populations that exhibit significant differences. Finally, we use this test to develop a clustering method that automatically identifies populations with similar dependence structures. They approaches, implemented in the Kcop R package, are demonstrated through numerical studies and real-world applications. This approach can be extended to the independent clustering in high dimension where work is ongoing.