A test for equality of two distributions via jackknife empirical likelihood and characteristic functions

The two-sample problem: testing the equality of two distributions is investigated. A jackknife empirical likelihood (JEL) test is proposed through incorporating characteristic functions, which reduces to a two-sample UU-statistic. When the dimension of data is fixed, the nonparametric Wilks’s theorem for the proposed JEL ratio statistics is established. When the dimension diverges with the sample size at a moderate rate, p=o(n1/3)p=o(n1/3), it is proved that under some mild conditions the normalized JEL ratio statistic has a standard normal limit. Moreover, when the dimension exceeds the sample size, p>np>n, an alternative version of JEL test is proposed. It is verified that under the null hypothesis this alternative version of JEL test has an asymptotical chi-squared distribution with two degrees of freedom. Some numerical results via simulation study and an analysis of a microarray dataset are presented and both confirm theoretical results empirically.