MMCTest—A Safe Algorithm for Implementing Multiple Monte Carlo Tests
提出MMCTest算法，通过序贯抽样以高概率保证与理想p值下的多重检验结果一致，支持FDR和FWER控制，可提前停止已决假设的抽样，计算效率优于传统方法。
ABSTRACT Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest , a sequential algorithm that gives, with arbitrarily high probability, the same classification as a specific multiple testing procedure applied to ideal p ‐values. The method can be used with a class of multiple testing procedures that include the Benjamini and Hochberg false discovery rate procedure and the Bonferroni correction controlling the familywise error rate. One of the key features of the algorithm is that it stops sampling for all the hypotheses that can already be decided as being rejected or non‐rejected. MMCTest can be interrupted at any stage and then returns three sets of hypotheses: the rejected, the non‐rejected and the undecided hypotheses. A simulation study motivated by actual biological data shows that MMCTest is usable in practice and that, despite the additional guarantee, it can be computationally more efficient than other methods.