Tests of uniformity on the hypersphere

E. García Portugués

We provide a general and tractable family of tests of uniformity on the hypersphere of arbitrary dimension. The family is constructed from powers of the chordal distances between pairs of observations. It connects and extends three particular tests: Rayleigh (1919), Pycke (2007, 2010), and Bakshaev (2010). The asymptotic null distributions of the new tests are obtained and, despite involving infinite sums of weighted chi-squared random variables, are shown to be tractable. Additionally, powers of the tests against generic local alternatives are provided. In particular, explicit powers against novel Cauchy-like distributions on the hypersphere, that are of independent interest, are derived. Numerical experiments corroborate the obtained theoretical results. Two real data applications of astronomical and biological nature illustrate the practical use of the tests for assessing uniformity on the two-dimensional sphere.

Keywords: Directional data, sphere, tests, uniformity

Scheduled

GT18 Non-parametric statistics I. Non-parametric hypothesis tests
June 9, 2022  10:10 AM
A15

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