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A stereographic test of spherical uniformity

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  • Fernández-de-Marcos, Alberto
  • García-Portugués, Eduardo

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.

Suggested Citation

  • Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2024. "A stereographic test of spherical uniformity," Statistics & Probability Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s0167715224001871
    DOI: 10.1016/j.spl.2024.110218
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    References listed on IDEAS

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    1. Eduardo García-Portugués & Davy Paindaveine & Thomas Verdebout, 2020. "On Optimal Tests for Rotational Symmetry Against New Classes of Hyperspherical Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1873-1887, December.
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