It is conventionally believed that a permutation test should ideally use all permutations. If this is computationally unaffordable, it is believed one should use the largest affordable Monte Carlo sample or (algebraic) subgroup of permutations. We challenge this belief by showing we can sometimes obtain dramatically more power by using a tiny subgroup. As the subgroup is tiny, this simultaneously comes at a much lower computational cost. We exploit this to improve the popular permutation-based Westfall & Young MaxT multiple testing method. We study the relative efficiency in a Gaussian location model, and find the largest gain in high dimensions.

翻译：传统观点认为，置换检验理想情况下应使用所有可能的排列。若计算代价过高无法实现，则建议采用可承受的最大蒙特卡洛样本或（代数）置换子群。我们通过证明在某些情况下使用极小置换子群能获得显著更高的统计功效，对这一传统认知提出挑战。由于子群规模微小，此方法同时大幅降低了计算成本。我们利用这一发现改进了基于置换的Westfall & Young MaxT多重检验方法。通过在高斯位置模型中的相对效率研究，发现高维场景下功效增益最为显著。