An empirical likelihood inference for the coefficient difference of a two-sample linear model with missing response data

In this paper, we use the empirical likelihood method to make inferences for the coefficient difference of a two-sample linear regression model with missing response data. The commonly used empirical likelihood ratio is not concave for this problem, so we append a natural and well-explained condition to the likelihood function and propose three types of restricted empirical likelihood ratios for constructing the confidence region of the parameter in question. It can be demonstrated that all three empirical likelihood ratios have, asymptotically, chi-squared distributions. Simulation studies are carried out to show the effectiveness of the proposed approaches in aspects of coverage probability and interval length. A real data set is analysed with our methods as an example.