Flexible Bayesian Estimation of Elliptical Copulas

Elliptical copulas provide flexibility in modeling the dependence structure of a random vector. They are often parameterized with a correlation matrix and a scalar function, called generator. The estimation of the generator can be challenging, because it is a functional parameter. In this article, we provide a rigorous approach to estimating the generator in a Bayesian framework, which is simpler, more robust, and outperforms existing estimation methods in the literature. A major contribution of this article is a robust method of evaluating the elliptical copula likelihood by using mixtures of B-spline densities. The Matlab code used for the simulation study is available in the supplementary material.