Measuring deviations from spherical symmetry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914274260025344 |
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| author | Bai, Lujia Dette, Holger |
| author_facet | Bai, Lujia Dette, Holger |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_18598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measuring deviations from spherical symmetry Bai, Lujia Dette, Holger Methodology Statistics Theory 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. |
| title | Measuring deviations from spherical symmetry |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2510.18598 |