Empirical likelihood test for diagonal symmetry

Abstract

Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the diagonal symmetry, which is consistent against any fixed alternatives. The test statistic developed in this paper is based on the difference of two U-statistics. By applying the jackknife empirical likelihood approach, the standard limiting chi-square distribution with degree freedom of one is established and is used to determine critical value and p-value of the test. Simulation studies show that our method is competitive in terms of empirical sizes and empirical powers.