Note on High Dimensional Spatial-Sign Test for One Sample Problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909988965842944 |
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| author | Zhao, Ping Feng, Long |
| author_facet | Zhao, Ping Feng, Long |
| contents | We revisit the null distribution of the high-dimensional spatial-sign test of Wang et al. (2015) under mild structural assumptions on the scatter matrix. We show that the standardized test statistic converges to a non-Gaussian limit, characterized as a mixture of a normal component and a weighted chi-square component. To facilitate practical implementation, we propose a wild bootstrap procedure for computing critical values and establish its asymptotic validity. Numerical experiments demonstrate that the proposed bootstrap test delivers accurate size control across a wide range of dependence settings and dimension-sample-size regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Note on High Dimensional Spatial-Sign Test for One Sample Problem Zhao, Ping Feng, Long Methodology We revisit the null distribution of the high-dimensional spatial-sign test of Wang et al. (2015) under mild structural assumptions on the scatter matrix. We show that the standardized test statistic converges to a non-Gaussian limit, characterized as a mixture of a normal component and a weighted chi-square component. To facilitate practical implementation, we propose a wild bootstrap procedure for computing critical values and establish its asymptotic validity. Numerical experiments demonstrate that the proposed bootstrap test delivers accurate size control across a wide range of dependence settings and dimension-sample-size regimes. |
| title | Note on High Dimensional Spatial-Sign Test for One Sample Problem |
| topic | Methodology |
| url | https://arxiv.org/abs/2601.08736 |