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TESTING February 23, 2026

Addressing parity blindness of data-driven Sobolev tests on the hypersphere

Authors

Marcio Reverbel

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.

Metadata

arXiv ID: 2602.19839
Provider: ARXIV
Primary Category: math.ST
Published: 2026-02-23
Fetched: 2026-02-24 04:38

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