错误发现率包络
False discovery rate envelopes
AI总结：
针对函数型多重检验中高度相关假设的 FDR 控制与可视化问题，提出基于重抽样的两类自适应单阈值图形包络方法，并用模拟和三个实例验证。
摘要：
错误发现率（FDR）是多重检验中控制错误发现数量的常用方式。目前已有多种可用于控制 FDR 的方法。然而，对于被离散化为 $m$ 个高度相关假设的函数型检验统计量，这些方法必须考虑函数域上分布的变化以及相关结构。此外，将检验统计量与其拒绝域或接受域一起可视化具有重要的实际意义。因此，本文旨在基于重抽样原则寻找一种能够控制 FDR 的图形包络，并通过一个简单规则检测所有单个假设的结果：当且仅当经验检验统计量位于包络之外时，该假设被拒绝。这种包络为检验结果提供了直观的解释，类似于最近发展的控制族系错误率的全局包络检验。为实现这一目标，本文开发了两种不同的自适应单阈值程序。通过大量模拟研究考察了它们的性能，并通过三个真实数据示例对这些新方法进行了说明。
英文摘要：
False discovery rate (FDR) is a common way to control the number of false discoveries in multiple testing. There are a number of approaches available for controlling FDR. However, for functional test statistics, which are discretized into $m$ highly correlated hypotheses, the methods must account for changes in distribution across the functional domain and correlation structure. Further, it is of great practical importance to visualize the test statistic together with its rejection or acceptance region. Therefore, the aim of this paper is to find, based on resampling principles, a graphical envelope that controls FDR and detects the outcomes of all individual hypotheses by a simple rule: the hypothesis is rejected if and only if the empirical test statistic is outside of the envelope. Such an envelope offers a straightforward interpretation of the test results, similarly as the recently developed global envelope testing which controls the family-wise error rate. Two different adaptive single threshold procedures are developed to fulfill this aim. Their performance is studied in an extensive simulation study. The new methods are illustrated by three real data examples.
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。
