Rank-Based Tests for Mutual Independence of High-Dimensional Random Vectors via $L_q$ Norm
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| Format: | Preprint |
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2026
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| _version_ | 1866918520937250816 |
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| author | Zhao, Ping Wang, Hongfei Feng, Long |
| author_facet | Zhao, Ping Wang, Hongfei Feng, Long |
| contents | We consider the problem of testing mutual independence among the components of a high-dimensional random vector. Building on the rank-based max-sum framework, we introduce fixed finite-$L_q$ power-sum statistics under three general classes of rank-based correlations: simple linear rank statistics, non-degenerate rank-based U-statistics and degenerate rank-based U-statistics. The proposed statistics interpolate between the dense-alternative sensitivity of the $L_2$ statistic and the sparse-alternative sensitivity of the $L_\infty$ statistic. We establish the asymptotic independence between any fixed finite-$L_q$ block and the corresponding $L_\infty$ statistic, and combine $L_2,L_4,L_6$ and $L_\infty$ p-values through a Cauchy rule. Numerical studies show that the resulting $L_{2,4,6,\infty}$ procedure is highly robust to the sparsity of the alternative and has strong empirical power across the considered designs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_25380 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rank-Based Tests for Mutual Independence of High-Dimensional Random Vectors via $L_q$ Norm Zhao, Ping Wang, Hongfei Feng, Long Methodology We consider the problem of testing mutual independence among the components of a high-dimensional random vector. Building on the rank-based max-sum framework, we introduce fixed finite-$L_q$ power-sum statistics under three general classes of rank-based correlations: simple linear rank statistics, non-degenerate rank-based U-statistics and degenerate rank-based U-statistics. The proposed statistics interpolate between the dense-alternative sensitivity of the $L_2$ statistic and the sparse-alternative sensitivity of the $L_\infty$ statistic. We establish the asymptotic independence between any fixed finite-$L_q$ block and the corresponding $L_\infty$ statistic, and combine $L_2,L_4,L_6$ and $L_\infty$ p-values through a Cauchy rule. Numerical studies show that the resulting $L_{2,4,6,\infty}$ procedure is highly robust to the sparsity of the alternative and has strong empirical power across the considered designs. |
| title | Rank-Based Tests for Mutual Independence of High-Dimensional Random Vectors via $L_q$ Norm |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.25380 |