Bivariate copulas defined from matrices

TL;DR

This paper introduces a semiparametric family of bivariate copulas constructed from matrices and orthonormal functions, allowing high dependence modeling without singularities and unifying various existing copula extensions.

Contribution

It presents a novel copula family based on matrices and orthonormal functions, capable of achieving near-perfect dependence and encompassing multiple existing copula types.

Findings

Can reach Spearman's Rho arbitrarily close to one

Includes extensions of FGM and partition-of-unity copulas

Framework for projecting arbitrary densities onto tensor product bases

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. Finally, it is also shown that projection of arbitrary densities of copulas onto tensor product bases can enter our framework.