High-dimensional Sobolev tests on hyperspheres

Fuente: arXiv
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Main Authors: Ebner, Bruno, García-Portugués, Eduardo, Verdebout, Thomas
Format: Preprint
Published: 2025
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author Ebner, Bruno
García-Portugués, Eduardo
Verdebout, Thomas
author_facet Ebner, Bruno
García-Portugués, Eduardo
Verdebout, Thomas
contents We derive the limit null distribution of the class of Sobolev tests of uniformity on the hypersphere when the dimension and the sample size diverge to infinity at arbitrary rates. The limiting non-null behavior of these tests is obtained for a sequence of integrated von Mises-Fisher local alternatives. The asymptotic results are applied to test for high-dimensional rotational symmetry and spherical symmetry. Numerical experiments illustrate the derived behavior of the uniformity and spherically symmetry tests under the null and under local and fixed alternatives.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10898
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle High-dimensional Sobolev tests on hyperspheres
Ebner, Bruno
García-Portugués, Eduardo
Verdebout, Thomas
Statistics Theory
Methodology
62G10, 62H11
We derive the limit null distribution of the class of Sobolev tests of uniformity on the hypersphere when the dimension and the sample size diverge to infinity at arbitrary rates. The limiting non-null behavior of these tests is obtained for a sequence of integrated von Mises-Fisher local alternatives. The asymptotic results are applied to test for high-dimensional rotational symmetry and spherical symmetry. Numerical experiments illustrate the derived behavior of the uniformity and spherically symmetry tests under the null and under local and fixed alternatives.
title High-dimensional Sobolev tests on hyperspheres
topic Statistics Theory
Methodology
62G10, 62H11
url https://arxiv.org/abs/2501.10898