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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14231 |
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| _version_ | 1866915864122490880 |
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| author | Zhao, Ping Yuan, Liangliang |
| author_facet | Zhao, Ping Yuan, Liangliang |
| contents | We study global inference for regression coefficients in high-dimensional linear models under potentially heavy-tailed errors. While sum-type tests are powerful for dense alternatives and max-type tests excel for sparse alternatives, practical applications rarely reveal the sparsity level, and many existing procedures rely on light-tail assumptions. Motivated by the Wilcoxon-score sum test of Feng et al. (2013) and the two Wilcoxon-score maximum tests of Xu and Zhou (2021), we establish under $H_0$ the asymptotic independence between the rank-based sum statistic and each max statistic. These joint limit results justify principled $p$-value aggregation, and we propose two adaptive rank-based maxsum tests via the Cauchy combination method (Liu and Xie, 2020). The proposed procedures inherit robustness from rank-based construction and adaptivity from combining dense- and sparse-sensitive components. Simulation studies confirm accurate size control and strong power across a wide range of error distributions and sparsity regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14231 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rank-based Maxsum test for high dimensional regression coefficient Zhao, Ping Yuan, Liangliang Methodology We study global inference for regression coefficients in high-dimensional linear models under potentially heavy-tailed errors. While sum-type tests are powerful for dense alternatives and max-type tests excel for sparse alternatives, practical applications rarely reveal the sparsity level, and many existing procedures rely on light-tail assumptions. Motivated by the Wilcoxon-score sum test of Feng et al. (2013) and the two Wilcoxon-score maximum tests of Xu and Zhou (2021), we establish under $H_0$ the asymptotic independence between the rank-based sum statistic and each max statistic. These joint limit results justify principled $p$-value aggregation, and we propose two adaptive rank-based maxsum tests via the Cauchy combination method (Liu and Xie, 2020). The proposed procedures inherit robustness from rank-based construction and adaptivity from combining dense- and sparse-sensitive components. Simulation studies confirm accurate size control and strong power across a wide range of error distributions and sparsity regimes. |
| title | Rank-based Maxsum test for high dimensional regression coefficient |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.14231 |