Abstract: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.
| Subjects: | Methodology (stat.ME) |
| Cite as: | arXiv:2605.25380 [stat.ME] |
| (or arXiv:2605.25380v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25380 arXiv-issued DOI via DataCite (pending registration) |
From: Long Feng [view email]
[v1]
Mon, 25 May 2026 03:09:44 UTC (1,047 KB)
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