Adaptive Test Procedure for High Dimensional Regression Coefficient
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908820202061824 |
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| author | Zhao, Ping Song, Fengyi Ma, Huifang |
| author_facet | Zhao, Ping Song, Fengyi Ma, Huifang |
| contents | We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging classical max-type and sum-type tests. We establish joint weak convergence of the extreme-value component and standardized $L$-statistics under mild conditions, yielding an asymptotic independence that justifies combining multiple $k$'s. An adaptive omnibus test is constructed via a Cauchy combination over a dyadic grid of $k$, and a wild bootstrap calibration is provided with theoretical guarantees. Simulations demonstrate accurate size and strong power across sparse and dense alternatives, including non-Gaussian designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07911 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Test Procedure for High Dimensional Regression Coefficient Zhao, Ping Song, Fengyi Ma, Huifang Applications We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging classical max-type and sum-type tests. We establish joint weak convergence of the extreme-value component and standardized $L$-statistics under mild conditions, yielding an asymptotic independence that justifies combining multiple $k$'s. An adaptive omnibus test is constructed via a Cauchy combination over a dyadic grid of $k$, and a wild bootstrap calibration is provided with theoretical guarantees. Simulations demonstrate accurate size and strong power across sparse and dense alternatives, including non-Gaussian designs. |
| title | Adaptive Test Procedure for High Dimensional Regression Coefficient |
| topic | Applications |
| url | https://arxiv.org/abs/2602.07911 |