An overview of uniformity tests on the hypersphere

Understand

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.