A stereographic test of spherical uniformity

Alberto Fernández-de-Marcos and Eduardo García-Portugués

Statistics & Probability Letters, 2024, vol. 215, issue C

Abstract: We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations.

Keywords: Spherical data; Stereographic projection; Uniformity tests (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110218

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