Testing axial symmetry around an unspecified direction
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915930194313216 |
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| author | Cholaquidis, Alejandro Cuesta-Albertos, Juan Fraiman, Ricardo Hernández-Banadik, Manuel |
| author_facet | Cholaquidis, Alejandro Cuesta-Albertos, Juan Fraiman, Ricardo Hernández-Banadik, Manuel |
| contents | We consider the problem of testing whether a multivariate distribution is axially symmetric about some unknown direction. Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of the covariance matrix, so the problem reduces to testing a finite set of candidate directions. For each candidate direction, we construct a Kolmogorov--Smirnov-type statistic based on projected data and sample splitting. We derive its asymptotic distribution in a triangular-array framework and establish bootstrap validity under suitable regularity conditions. This leads to a feasible testing procedure for axial symmetry when the symmetry direction is unspecified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09317 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Testing axial symmetry around an unspecified direction Cholaquidis, Alejandro Cuesta-Albertos, Juan Fraiman, Ricardo Hernández-Banadik, Manuel Statistics Theory We consider the problem of testing whether a multivariate distribution is axially symmetric about some unknown direction. Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of the covariance matrix, so the problem reduces to testing a finite set of candidate directions. For each candidate direction, we construct a Kolmogorov--Smirnov-type statistic based on projected data and sample splitting. We derive its asymptotic distribution in a triangular-array framework and establish bootstrap validity under suitable regularity conditions. This leads to a feasible testing procedure for axial symmetry when the symmetry direction is unspecified. |
| title | Testing axial symmetry around an unspecified direction |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2604.09317 |