The properties of the cross-match estimate and split sampling

Abstract

By noting the connection with k-sample U-statistics, we find a simple decomposition of the variance of the cross-match estimate, which can be regarded as a generalization of Efron and Stein. We apply the decomposition in assessing efficiencies of several plans of using the weighted samples from an importance scheme. The applications of the formula to multiple imputations lead to a method of crossing jointly imputed data to gain more accuracy.