Jackknife empirical likelihood of error variance for partially linear varying-coefficient model with missing covariates

In this paper, we apply the profile least-square method and inverse probability weighted method to define estimation of the error variance in partially linear varying-coefficient model when the covariates are missing at random. At the same time, we construct a jackknife estimator and jackknife empirical likelihood (JEL) statistic of the error variance, respectively. It is proved that the proposed estimators are asymptotical normality and the JEL statistic admits a limiting standard chi-square distribution. A simulation study is conducted to compare the JEL method with the normal approximation approach in terms of coverage probabilities and average interval lengths, and a comparison of the proposed estimators is done based on sample means, biases and mean square errors under different settings. Subsequently, a real data set is analyzed for illustration of the proposed methods.