In contemporary problems involving genetic or neuroimaging data, thousands of hypotheses need to be tested. Due to their high power, and finite sample guarantees on type-1 error under weak assumptions, Monte-Carlo permutation tests are often considered as gold standard for these settings. However, the enormous computational effort required for (thousands of) permutation tests is a major burden. Recently, Fischer and Ramdas (2024) constructed a permutation test for a single hypothesis in which the permutations are drawn sequentially one-by-one and the testing process can be stopped at any point without inflating the type I error. They showed that the number of permutations can be substantially reduced (under null and alternative) while the power remains similar. We show how their approach can be modified to make it suitable for a broad class of multiple testing procedures. In particular, we discuss its use with the Benjamini-Hochberg procedure and illustrate the application on a large dataset.

翻译：在涉及遗传或神经影像数据的当代问题中，需要检验数千个假设。由于蒙特卡洛置换检验具有较高的统计功效，且在弱假设条件下对第一类错误具有有限样本保证，因此通常被视为这些场景中的黄金标准。然而，（数千次）置换检验所需的巨大计算负担是一个主要挑战。近期，Fischer与Ramdas（2024）针对单一假设构建了一种置换检验方法，其中置换过程可逐次顺序抽取，且检验过程可在任意时刻终止而不增加第一类错误率。他们证明该方法（在零假设与备择假设下）能显著减少置换次数，同时保持相近的统计功效。我们展示如何改进其方法，使其适用于广泛类别的多重检验程序。特别地，我们讨论了该方法与Benjamini-Hochberg程序结合的应用，并通过大型数据集进行实例说明。