{"ID":2852252,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.18598","arxiv_id":"2510.18598","title":"Measuring deviations from spherical symmetry","abstract":"Most of the work on checking spherical symmetry assumptions on the distribution of the $p$-dimensional random vector $Y$ 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 $\\big (\\|Y\\|, Y/ \\|Y\\| )^\\top $ and its best approximation by a distribution of a vector $\\big (\\|Y_s\\|, Y_s/ \\|Y_s \\| )^\\top $ corresponding to a random vector $Y_s$ 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.","short_abstract":"Most of the work on checking spherical symmetry assumptions on the distribution of the $p$-dimensional random vector $Y$ 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 symmetr...","url_abs":"https://arxiv.org/abs/2510.18598","url_pdf":"https://arxiv.org/pdf/2510.18598v2","authors":"[\"Lujia Bai\",\"Holger Dette\"]","published":"2025-10-21T12:56:38Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}