Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application

Abstract

The exchangeability and radial symmetry assumptions on the dependence structure of the multivariate data are restrictive in practical situations where the variables of interest are not likely to be associated to each other in an identical manner. In this paper, we propose a flexible class of multivariate skew normal copulas to model high-dimensional asymmetric dependence patterns. The proposed copulas have two sets of parameters capturing asymmetric dependence, one for association between the variables and the other for skewness of the variables. In order to efficiently estimate the two sets of parameters, we introduce the block coordinate ascent algorithm and discuss its convergence property. The proposed class of multivariate skew normal copulas is illustrated using a real data set.