A Bayesian Semiparametric Gaussian Copula Approach to a Multivariate Normality Test
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In this paper, a Bayesian semiparametric copula approach is used to model the underlying multivariate distribution F_true. First, the Dirichlet process is constructed on the unknown marginal distributions of F_true. Then a Gaussian copula model is utilized to capture the dependence structure of F_true. 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.
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