Paper
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
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.19839v1</id>\n <title>Addressing parity blindness of data-driven Sobolev tests on the hypersphere</title>\n <updated>2026-02-23T13:40:39Z</updated>\n <link href='https://arxiv.org/abs/2602.19839v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.19839v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.ST'/>\n <published>2026-02-23T13:40:39Z</published>\n <arxiv:comment>6 pages, 1 figure, submitted to Statistics & Probability Letters</arxiv:comment>\n <arxiv:primary_category term='math.ST'/>\n <author>\n <name>Marcio Reverbel</name>\n </author>\n </entry>"
}