High-Dimensional Two-Sample Test for Elliptical Symmetry Distribution
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915979216289792 |
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| author | Feng, Long Wang, Hongfei |
| author_facet | Feng, Long Wang, Hongfei |
| contents | We study the high-dimensional two-sample location problem under elliptical symmetry with arbitrary dependence in the scatter matrix. Existing spatial-sign procedures are attractive for heavy-tailed data, but their null calibration is tied to weakly dependent scatter matrices and their diagonal standardization does not, in general, recover the diagonal shape under strong dependence. We propose a new spatial-sign test based on coordinatewise pairwise-difference quantile scales. The new diagonal standardizer is location free, requires no positive moment condition on the radial variable, and estimates the diagonal of the elliptical shape up to a scalar specific to the sample, which disappears after spatial normalization. For the resulting full-sample statistic, we derive an explicit-rate stochastic expansion, establish a general weighted chi-square null distribution under arbitrary correlation structure, justify an empirical diagonal-deletion correction, and show that a Rademacher wild bootstrap consistently estimates the null law. The usual normal approximation appears only as a special case when no eigenvalue dominates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03265 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Two-Sample Test for Elliptical Symmetry Distribution Feng, Long Wang, Hongfei Methodology We study the high-dimensional two-sample location problem under elliptical symmetry with arbitrary dependence in the scatter matrix. Existing spatial-sign procedures are attractive for heavy-tailed data, but their null calibration is tied to weakly dependent scatter matrices and their diagonal standardization does not, in general, recover the diagonal shape under strong dependence. We propose a new spatial-sign test based on coordinatewise pairwise-difference quantile scales. The new diagonal standardizer is location free, requires no positive moment condition on the radial variable, and estimates the diagonal of the elliptical shape up to a scalar specific to the sample, which disappears after spatial normalization. For the resulting full-sample statistic, we derive an explicit-rate stochastic expansion, establish a general weighted chi-square null distribution under arbitrary correlation structure, justify an empirical diagonal-deletion correction, and show that a Rademacher wild bootstrap consistently estimates the null law. The usual normal approximation appears only as a special case when no eigenvalue dominates. |
| title | High-Dimensional Two-Sample Test for Elliptical Symmetry Distribution |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.03265 |