Empirical Likelihood for Multidimensional Linear Model with Missing Responses

Imputation is a popular technique for handling missing data especially for plenty of missing values. Usually, the empirical log-likelihood ratio statistic under imputation is 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 with missing response data, and the resulting empirical likelihood ratio is asymptotically chi-squared. However, it may suffer from the "the curse of high dimension" in multidimensional linear regression models for the nonparametric estimator of selection probability function. In this paper, a parametric selection probability function is introduced to avoid the dimension problem. With the similar bias-corrected method, the proposed empirical likelihood statistic is asymptotically chi-squared when the selection probability is specified correctly and even asymptotically scaled chi-squared when specified incorrectly. In addition, our empirical likelihood estimator is always consistent whether the selection probability is specified correctly or not, and will achieve full efficiency when specified correctly. A simulation study indicates that the proposed method is comparable in terms of coverage probabilities.