A new distance based on pairwise inner products yields a test for spherical uniformity that achieves minimax optimal detection rates across multiple high-dimensional parametric models, including cases without densities.
An overview of uniformity tests on the hypersphere
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abstract
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different from uniformity. We review in this article a reasonably exhaustive collection of uniformity tests for assessing uniformity in the hypersphere. Specifically, we review the classical circular-specific tests, the large class of Sobolev tests with its many notable particular cases, some recent alternative tests, and novel results in the high-dimensional low-sample size case. A reasonably comprehensive bibliography on the topic is provided.
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2025 1verdicts
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Detecting non-uniform patterns on high-dimensional hyperspheres
A new distance based on pairwise inner products yields a test for spherical uniformity that achieves minimax optimal detection rates across multiple high-dimensional parametric models, including cases without densities.