Semi-empiricial Likelihood Confidence Intervals for the Differences of Two Populations Based on Fractional Imputation

Suppose that there axe two populations x and y with missing data on both of them, where x has a distribution function F(.) which is unknown and y has form depending on some unknown parameter θ. Fractional imputation is used to fill in missing data. The asymptotic distributions of the semi-empirical likelihood ration statistic are obtained under some mild conditions. Then, empirical likelihood confidence intervals on the differences of x and y are constructed.