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.
This test is also based on a U-statistic of the data points, but with a quadratic inner product kernel, i.e
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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.