Fitting copulas in the case of missing data

In this paper we deal with parametric estimation of the copula in the case of missing data. The data items with the same pattern of complete and missing data are combined into a subset. This approach corresponds to the MCAR model for missing data. We construct a specific Cramér–von Mises statistic as a sum of such statistics for the several missing data patterns. The minimization of the statistic gives the estimators for the parameters. We prove asymptotic normality of the parameter estimators and of the Cramér–von Mises statistic.