Consider testing multiple hypotheses in the setting where the p-values of all hypotheses are unknown and thus have to be approximated using Monte Carlo simulations. One class of algorithms published in the literature for this scenario provides guarantees on the correctness of their testing result through the computation of confidence statements on all approximated p-values. This article focuses on the expected runtime of such algorithms and derives a variety of finite and infinite expected runtime results.

中文翻译：

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关于具有有限误差的多个测试算法的预期运行时间

考虑在所有假设的 p 值未知的设置中测试多个假设，因此必须使用蒙特卡罗模拟进行近似。文献中针对该场景发布的一类算法通过计算所有近似 p 值的置信度陈述来保证其测试结果的正确性。本文重点讨论此类算法的预期运行时间，并推导出各种有限和无限的预期运行时间结果。