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Bivariate copulas defined from matrices

Cécile Amblard 1 Stephane Girard 2 Ludovic Menneteau 3
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it encompasses several extensions of FGM copulas as well as copulas based on partition of unity such as Bernstein or checkerboard copulas. It is also shown that projection of arbitrary densities of copulas onto tensor product bases can enter our framework.Finally, two estimators of copulas are introduced and theirfinite sample behaviours are compared on simulated data.
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Cécile Amblard, Stephane Girard, Ludovic Menneteau. Bivariate copulas defined from matrices. 2014. ⟨hal-00875303v2⟩

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