Semi-Empiricial Likelihood Confidence Intervals for the Differences of Two Populations Based on Fractional Imputation (Communications in Mathematical Research, 2021)
Suppose that there are two populations $x$ and $y$ with missing data onboth of them, where $x$ has a distribution function $F(·)$ which is unknown and $y$ hasa distribution function $G_θ(·)$ with a probability density function $g_θ(·)$ with knownform depending on some unknown parameter $θ$. Fractional imputation is used tofill in missing data. The asymptotic distributions of the semi-empirical likelihoodration statistic are obtained under some mild conditions. Then, empirical likelihoodconfidence intervals on the differences of $x$ and $y$ are constructed.