More efficient exact group invariance testing: using a representative subgroup
提出用固定子群替代随机子集进行群不变性检验，在广义位置模型中能检测更低的信噪比，并在置换多重检验中大幅减少所需置换次数。
Summary We consider testing invariance of a distribution under an algebraic group of transformations, such as permutations or sign flips. As such groups are typically huge, tests based on the full group are often computationally infeasible. Hence, it is standard practice to use a random subset of transformations. We improve upon this by replacing the random subset with a strategically chosen, fixed subgroup of transformations. In a generalized location model, we show that the resulting tests are often consistent for lower signal-to-noise ratios. Moreover, we establish an analogy between the power improvement and switching from a t-test to a Z-test under normality. Importantly, in permutation-based multiple testing, the efficiency gain with our approach can be huge, since we attain the same power with many fewer permutations.