Empirical likelihood for response differences in two linear regression models with missing data

Abstract

Consider two linear models Xi = U′iβ + eiYj = V′jγ + ηj with response variables missing at random. In this paper, we assume that X, Y are missing at random (MAR) and use the inverse probability weighted imputation to produce ‘complete’ data sets for X and Y. Based on these data sets, we construct an empirical likelihood (EL) statistic for the difference of X and Y (denoted as Δ), and show that the EL statistic has the limiting distribution of χ12, which is used to construct a confidence interval for Δ. Results of a simulation study on the finite sample performance of EL-based confidence intervals on Δ are reported.