Empirical Likelihood of Quantile Difference with Missing Response When High-dimensional Covariates Are Present.

We, in this paper, investigate two-sample quantile difference by empirical likelihood method when the responses with high-dimensional covariates of the two populations are missing at random. In particular, based on sufficient dimension reduction technique, we construct three empirical log-likelihood ratios for the quantile difference between two samples by using inverse probability weighting imputation, regression imputation as well as augmented inverse probability weighting imputation, respectively, and prove their asymptotic distributions. At the same time, we give a test to check whether two populations have the same distribution. A simulation study is carried out to investigate finite sample behavior of the proposed methods too. [ABSTRACT FROM AUTHOR]