On empirical likelihood for linear models with missing responses

Suppose that we have a linear regression model Y = X ′ β + ν 0 ( X ) ε with random error ε , where X is a random design variable and is observed completely, and Y is the response variable and some Y-values are missing at random (MAR). In this paper, based on the ‘complete’ data set for Y after inverse probability weighted imputation, we construct empirical likelihood statistics on EY and β which have the χ 2 -type limiting distributions under some new conditions compared with Xue (2009). Our results broaden the applicable scope of the approach combined with Xue (2009).