Empirical Likelihood for Multidimensional Linear Model with Missing Responses

Imputation is a popular technique for handling missing data especially for plentyof missing values. Usually, the empirical log-likelihood ratio statistic under imputationis asymptotically scaled chi-squared because the imputing data are not i.i.d.Recently, a bias-corrected technique is used to study linear regression model withmissing response data, and the resulting empirical likelihood ratio is asymptoticallychi-squared. However, it may suffer from the “the curse of high dimension” in multidimensionallinear regression models for the nonparametric estimator of selectionprobability function. In this paper, a parametric selection probability function isintroduced to avoid the dimension problem. With the similar bias-corrected method,the proposed empirical likelihood statistic is asymptotically chi-squared when the selectionprobability is specified correctly and even asymptotically scaled chi-squaredwhen specified incorrectly. In addition, our empirical likelihood estimator is alwaysconsistent whether the selection probability is specified correctly or not, and willachieve full efficiency when specified correctly. A simulation study indicates thatthe proposed method is comparable in terms of coverage probabilities