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arXiv · 2008.10767

A Cram\'er-von Mises test of uniformity on the hypersphere

Eduardo García-Portugués·Paula Navarro-Esteban·Juan A. Cuesta-Albertos
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Abstract

Testing uniformity of a sample supported on the hypersphere is one of the first steps when analysing multivariate data for which only the directions (and not the magnitudes) are of interest. In this work, a projection-based Cram\'er-von Mises test of uniformity on the hypersphere is introduced. This test can be regarded as an extension of the well-known Watson test of circular uniformity to the hypersphere. The null asymptotic distribution of the test statistic is obtained and, via numerical experiments, shown to be tractable and practical. A novel study on the uniformity of the distribution of craters on Venus illustrates the usage of the test.

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Eduardo García-Portugués, Paula Navarro-Esteban, Juan A. Cuesta-Albertos. 2020-08-25. A Cram\'er-von Mises test of uniformity on the hypersphere. https://doi.org/10.1007/978-3-030-69944-4_12

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