In this paper, we analyze the effects of the strategic selection of an algebraic subgroup for use in the permutation- or group invariance-based Westfall \& Young maxT multiple testing method. We report the surprising observation that a tiny subgroup can produce a version of the maxT method that dramatically outperforms the method based on entire group or on a large number of Monte Carlo draws. To explain these findings, we characterize the power of the maxT method based on a strategically selected subgroup and the entire group in a Gaussian location model with $p$ tests and $n$ observations. By studying the relative efficiency, we find that the power difference is largest in high dimensional settings where $n^{-1/2} \log p$ is large.

翻译：本文分析了在基于置换或群不变性的Westfall & Young maxT多重假设检验方法中，策略性选择代数子群的影响。我们报告了一个惊人发现：微小子群可产生一种版本的maxT方法，其表现远优于基于整个群组或大量蒙特卡洛抽样的方法。为解释这些发现，我们在包含p个检验和n个观测的高斯位置模型中，刻画了基于策略性选择的子群与整个群组的maxT方法的效力。通过研究相对效率，我们发现当n^{-1/2} log p较大时，效力差异在高维场景中最为显著。