Testing for diagonal symmetry based on center-outward ranking

Sakineh Dehghan, Mohammad Reza Faridrohani () and Zahra Barzegar
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Sakineh Dehghan: Shahid Beheshti University
Mohammad Reza Faridrohani: Shahid Beheshti University
Zahra Barzegar: Saman Insurance Company

Statistical Papers, 2023, vol. 64, issue 1, No 12, 255-283

Abstract: Abstract 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.

Keywords: Asymptotically distribution-free; Center-outward ranking; Diagonal symmetry; Depth function (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01316-w

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