寻找具有错误发现率控制的分布
Finding Distributions that Differ, with False Discovery Rate Control
AI总结：
本文提出了一种分布无关的多重检验方法，用于识别与参考分布不同的分布，并通过模拟和实际数据验证其有效性。
摘要：
我们考虑了将参考分布与其他多个分布进行比较的问题。给定来自参考组和比较组的样本，我们旨在识别出那些分布与参考组分布不同的比较组。将此视为多重检验问题，我们引入了一种方法，该方法能够提供精确的、分布无关的错误发现率控制。为此，我们引入了批次符合p值的概念，并证明它们在组间满足正回归依赖性[Benjamini和Yekutieli，2001]，从而通过Benjamini-Hochberg程序实现错误发现率的控制。正回归依赖性的证明引入了一种新的技术，用于诱导构造具有几乎必然支配性的排名向量。我们通过模拟评估所提出方法的性能，在某些情况下，尽管是分布无关的，它们的性能与了解数据生成正态分布的方法相当；并且在某些情况下，其功率高于基于符合非分布检测的直接方法。此外，我们在肝炎C治疗数据集上展示了我们的方法，可以识别出具有大治疗效应的患者组；并在当前人口调查数据集中，可以识别出具有长工作时间的子群体。
英文摘要：
We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that of the reference group. Viewing this as a multiple testing problem, we introduce a methodology that provides exact, distribution-free control of the false discovery rate. To do so, we introduce the concept of batch conformal p-values and demonstrate that they satisfy positive regression dependence across the groups [Benjamini and Yekutieli, 2001], thereby enabling control of the false discovery rate through the Benjamini-Hochberg procedure. The proof of positive regression dependence introduces a novel technique for the inductive construction of rank vectors with almost sure dominance under exchangeability. We evaluate the performance of the proposed procedure through simulations, where, despite being distribution-free, in some cases they show performance comparable to methods with knowledge of the data-generating normal distribution; and further have more power than direct approaches based on conformal out-of-distribution detection. Further, we illustrate our methods on a Hepatitis C treatment dataset, where they can identify patient groups with large treatment effects; and on the Current Population Survey dataset, where they can identify sub-population with long work hours.
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。
