Empirical Likelihood‐based Inference in Linear Models with Missing Data

Abstract

The missing response problem in linear regression is studied. An adjusted empirical likelihood approach to inference on the mean of the response variable is developed. A non‐parametric version of Wilks's theorem for the adjusted empirical likelihood is proved, and the corresponding empirical likelihood confidence interval for the mean is constructed. With auxiliary information, an empirical likelihood‐based estimator with asymptotic normality is defined and an adjusted empirical log‐likelihood function with asymptotic χ2 is derived. A simulation study is conducted to compare the adjusted empirical likelihood methods and the normal approximation methods in terms of coverage accuracies and average lengths of the confidence intervals. Based on biases and standard errors, a comparison is also made between the empirical likelihood‐based estimator and related estimators by simulation. Our simulation indicates that the adjusted empirical likelihood methods perform competitively and the use of auxiliary information provides improved inferences.