Estimating Gaussian Copulas with Missing Data with and without Expert Knowledge

In this work, we present a rigorous application of the Expectation Maximization algorithm to determine the marginal distributions and the dependence structure in a Gaussian copula model with missing data. We further show how to circumvent a priori assumptions on the marginals with semiparametric modeling. Further, we outline how expert knowledge on the marginals and the dependency structure can be included. A simulation study shows that the distribution learned through this algorithm is closer to the true distribution than that obtained with existing methods and that the incorporation of domain knowledge provides benefits.