Empirical Likelihood Test for Diagonal Symmetry

TL;DR

This paper introduces a nonparametric energy distance-based test for diagonal symmetry, utilizing U-statistics and jackknife empirical likelihood, with proven asymptotic distribution and competitive performance in simulations.

Contribution

It develops a novel nonparametric test for diagonal symmetry using energy distance and jackknife empirical likelihood, with a proven chi-square distribution under the null hypothesis.

Findings

Test is consistent against fixed alternatives.

Method has competitive empirical size and power.

Asymptotic chi-square distribution is established.

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.