Adaptive L-tests for high dimensional independence
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911402632937472 |
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| author | Zhao, Ping Ma, Huifang |
| author_facet | Zhao, Ping Ma, Huifang |
| contents | Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual independence based on $L$-statistics. We establish the asymptotic distribution of the proposed test when the order parameter $k$ is fixed, and prove asymptotic normality when $k$ diverges with the dimension. Moreover, we show the asymptotic independence of the fixed-$k$ and diverging-$k$ statistics, enabling their combination through the Cauchy method. The resulting adaptive test is both theoretically justified and practically powerful across a wide range of alternatives. Simulation studies demonstrate the advantages of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive L-tests for high dimensional independence Zhao, Ping Ma, Huifang Applications Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual independence based on $L$-statistics. We establish the asymptotic distribution of the proposed test when the order parameter $k$ is fixed, and prove asymptotic normality when $k$ diverges with the dimension. Moreover, we show the asymptotic independence of the fixed-$k$ and diverging-$k$ statistics, enabling their combination through the Cauchy method. The resulting adaptive test is both theoretically justified and practically powerful across a wide range of alternatives. Simulation studies demonstrate the advantages of our method. |
| title | Adaptive L-tests for high dimensional independence |
| topic | Applications |
| url | https://arxiv.org/abs/2601.19688 |