Addressing parity blindness of data-driven Sobolev tests on the hypersphere
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911463023575040 |
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| author | Reverbel, Marcio |
| author_facet | Reverbel, Marcio |
| contents | We study the asymptotic behavior of the data-driven Sobolev test for testing uniformity on the (hyper)sphere. We show that it can be blind to certain contiguous alternatives and propose a simple modification of the test statistic. This adapted test retains consistency under fixed alternatives and achieves non-trivial asymptotic power against contiguous alternatives for which the original test fails. Simulation results support our theoretical findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_19839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Addressing parity blindness of data-driven Sobolev tests on the hypersphere Reverbel, Marcio Statistics Theory 62F03, 62F05, 62H11 (Primary) We study the asymptotic behavior of the data-driven Sobolev test for testing uniformity on the (hyper)sphere. We show that it can be blind to certain contiguous alternatives and propose a simple modification of the test statistic. This adapted test retains consistency under fixed alternatives and achieves non-trivial asymptotic power against contiguous alternatives for which the original test fails. Simulation results support our theoretical findings. |
| title | Addressing parity blindness of data-driven Sobolev tests on the hypersphere |
| topic | Statistics Theory 62F03, 62F05, 62H11 (Primary) |
| url | https://arxiv.org/abs/2602.19839 |