Empirical likelihood for linear regression models with missing responses

To make inference on β(∈Rp) in a linear regression model Yi=xi′β+ϵi with missing responses, Wang and Rao [Wang, Q., Rao, J.N.K., 2001. Empirical likelihood for linear regression models under imputation for missing responses. Canad. J. Statist. 29, 597–608.] constructed an empirical likelihood (EL) statistic based on the ‘complete’ data set after linear regression imputation which is asymptotically a sum of weighted χ12 variables with unknown weights. In this paper, we use a new method to produce a ‘complete’ data set for YY. Based on this data set, we construct an EL statistic on ββ, and show that the EL statistic has the limiting distribution of χp2 which is used to construct confidence region on ββ without adjustment. Results of a simulation study on the finite sample performance of EL-based confidence region on ββ are reported.