Addressing parity blindness of data-driven Sobolev tests on the hypersphere
Statistics Theory
2026-02-24 v1 Statistics Theory
Abstract
We study the asymptotic behavior of the data-driven Sobolev test for testing uniformity on the (hyper)sphere. We show that it can be blind to certain contiguous alternatives and propose a simple modification of the test statistic. This adapted test retains consistency under fixed alternatives and achieves non-trivial asymptotic power against contiguous alternatives for which the original test fails. Simulation results support our theoretical findings.
Keywords
Cite
@article{arxiv.2602.19839,
title = {Addressing parity blindness of data-driven Sobolev tests on the hypersphere},
author = {Marcio Reverbel},
journal= {arXiv preprint arXiv:2602.19839},
year = {2026}
}
Comments
6 pages, 1 figure, submitted to Statistics & Probability Letters