Multivariate Skew Normal Copula for Non-exchangeable Dependence

The exchangeability assumption on the dependence structure of the multivariate data is 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 non-exchangeable dependence patterns. The proposed copulas have two sets of parameters capturing non-exchangeable 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. The proposed class of multivariate skew normal copulas is illustrated using a real data set.