A stereographic test of spherical uniformity
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917741991034880 |
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| author | Fernández-de-Marcos, Alberto García-Portugués, Eduardo |
| author_facet | Fernández-de-Marcos, Alberto García-Portugués, Eduardo |
| contents | We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stereographic test of spherical uniformity Fernández-de-Marcos, Alberto García-Portugués, Eduardo Statistics Theory 62G10, 62H11 We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations. |
| title | A stereographic test of spherical uniformity |
| topic | Statistics Theory 62G10, 62H11 |
| url | https://arxiv.org/abs/2405.13531 |