Kavli Affiliate: Feng Long
| Summary:
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.
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