Empirical Likelihood Test for Diagonal Symmetry

Yongli Sang; Xin Dang

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arXiv · 1908.06892

Empirical Likelihood Test for Diagonal Symmetry

Yongli Sang·Xin Dang

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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.

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Yongli Sang, Xin Dang. 2019-08-19. Empirical Likelihood Test for Diagonal Symmetry. https://arxiv.org/abs/1908.06892

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