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arXiv · 2405.13531

A stereographic test of spherical uniformity

Alberto Fernández-de-Marcos·Eduardo García-Portugués
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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.

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Alberto Fernández-de-Marcos, Eduardo García-Portugués. 2024-05-22. A stereographic test of spherical uniformity. https://doi.org/10.1016/j.spl.2024.110218

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