A Bayesian Semiparametric Gaussian Copula Approach to a Multivariate Normality Test

In this paper, a Bayesian semiparametric copula approach is used to model the underlying multivariate distribution Ftrue. First, the Dirichlet process is constructed on the unknown marginal distributions of Ftrue. Then a Gaussian copula model is utilized to capture the dependence structure of Ftrue. As a result, a Bayesian multivariate normality test is developed by combining the relative belief ratio and the Energy distance. Several interesting theoretical results of the approach are derived. Finally, through several simulated examples and a real data set, the proposed approach reveals excellent performance.