In this paper, we consider the problem of testing for the equality of two distributions in high dimension. We investigate the performance of empirical likelihood and Jackknife empirical likelihood approach for this problem. The EL test statistics is based on the kernel type representation of the equality of distributions in a reproducing kernel Hilbert space (RKHS). The Wilks Theorem of both of EL and JEL tests are established. Our test statistic is robust to the high dimensional case. Various data experiments with Laplace kernel and Gaussian kernel assess the performance of proposed approaches.
