Multivariate Normal Inference based on Singly Imputed Synthetic Data under Plug-in Sampling

In this paper we consider singly imputed synthetic data generated via plug-in sampling under the multivariate normal model. Based on the observed synthetic dataset, we derive a statistical test for the generalized variance, the sphericity test, a test for independence between two subsets of variables, and a test for the regression of one set of variables on the other. The procedures are based on finite sample theory.