Jackknife empirical likelihood for the error variance in linear errors-in-variables models with missing data

Measurement errors and missing data are often arise in practice. Under this circumstance, we focus on using jackknife empirical likelihood (JEL) and adjust jackknife empirical likelihood (AJEL) methods to construct confidence intervals for the error variance in linear models. Based on residuals of the models, the biased-corrected inverse probability weighted estimator of the error variance is introduced. Furthermore, we propose the jackknife estimator, jackknife and adjust jackknife empirical log-likelihood ratios of the error variance and establish their asymptotic distributions. Simulation studies in terms of coverage probability and average length of confidence intervals are conducted to evaluate the proposed method. A real data set is used to illustrate the proposed JEL and AJEL methods.