Measuring deviations from spherical symmetry
Methodology
2026-01-26 v2 Statistics Theory
Statistics Theory
Abstract
Most of the work on checking spherical symmetry assumptions on the distribution of the -dimensional random vector has its focus on statistical tests for the null hypothesis of exact spherical symmetry. In this paper, we take a different point of view and propose a measure for the deviation from spherical symmetry, which is based on the minimum distance between the distribution of the vector and its best approximation by a distribution of a vector corresponding to a random vector with a spherical distribution. We develop estimators for the minimum distance with corresponding statistical guarantees (provided by asymptotic theory) and demonstrate the applicability of our approach by means of a simulation study and a real data example.
Cite
@article{arxiv.2510.18598,
title = {Measuring deviations from spherical symmetry},
author = {Lujia Bai and Holger Dette},
journal= {arXiv preprint arXiv:2510.18598},
year = {2026}
}