Testing for diagonal symmetry based on center-outward ranking

This paper aims to propose a new class of permutation-invariant tests for diagonal symmetry around a known point based on the center-outward depth ranking. The asymptotic behavior of the proposed tests under the null distribution is derived. The performance of the proposed tests is assessed through a Monte Carlo study. The results show that the tests perform well comparing other procedures in terms of empirical sizes and empirical powers. We demonstrated that the proposed class includes the celebrated Wilcoxon signed-rank test as a special case in the univariate setting. Finally, we apply the tests to a well-known data set to illustrate the method developed in this paper.

Automated summary

This paper proposes a new class of permutation-invariant tests based on center-outward depth ranking to test diagonal symmetry around a known point. The asymptotic behavior of the tests under the null distribution is derived, and their performance is evaluated through a Monte Carlo study. The results show that the tests outperform other procedures in terms of empirical sizes and powers. The paper also demonstrates that the proposed class includes the well-known Wilcoxon signed-rank test as a special case in the univariate setting. Finally, the tests are applied to a well-known dataset to illustrate the method developed in this paper.