太多，太不可能：测试联合假设和封闭测试快捷方式
Too Many, Too Improbable: testing joint hypotheses and closed testing shortcuts
摘要：
假设检验是实证科学的一个重要组成部分，多重检验以及来自多个检验的证据的组合是持续的研究领域。在这篇文章中，我们考虑的问题相结合的多个假设检验的结果，i）测试全局假设和ii）进行边际推理，同时控制k-FWER。我们提出了一个新的家庭的联合假设的组合检验，称为“太多，太不可能”（TMTI）的统计，我们通过模拟显示，有更高的权力比其他组合测试对许多替代品。此外，我们证明了一个大的家庭的组合测试-其中包括我们提出的，但也有其他组合测试-承认二次捷径时，用于封闭的测试程序，控制FWER强。我们开发了一种算法，该算法是线性的假设的数量，用于获得置信度集的数量之间的假假设的集合的假设和一个算法，该算法是立方的数量的假设，用于控制的k-FWER为任何k大于1。
英文摘要：
Hypothesis testing is a key part of empirical science and multiple testing as well as the combination of evidence from several tests are continued areas of research. In this article we consider the problem of combining the results of multiple hypothesis tests to i) test global hypotheses and ii) make marginal inference while controlling the k-FWER. We propose a new family of combination tests for joint hypotheses, called the 'Too Many, Too Improbable' (TMTI) statistics, which we show through simulation to have higher power than other combination tests against many alternatives. Furthermore, we prove that a large family of combination tests -- which includes the one we propose but also other combination tests -- admits a quadratic shortcut when used in a Closed Testing Procedure, which controls the FWER strongly. We develop an algorithm that is linear in the number of hypotheses for obtaining confidence sets for the number of false hypotheses among a collection of hypotheses and an algorithm that is cubic in the number of hypotheses for controlling the k-FWER for any k greater than one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
