论文标题
错误的发现率信封
False discovery rate envelopes
论文作者
论文摘要
错误的发现率（FDR）是控制多个测试中错误发现数量的常见方法。有许多可用于控制FDR的方法。但是，对于离散为$ M $高度相关的假设的功能测试统计数据，该方法必须考虑到功能域和相关结构之间的分布的变化。此外，可视化测试统计数据以及其拒绝或接受区域非常重要。因此，本文的目的是基于重新采样原理找到一个图形包络，该图形信封可以控制FDR并通过一个简单的规则检测所有单个假设的结果：仅当经验测试统计量之外，该假设才被拒绝。这样的信封对测试结果提供了直接的解释，就像最近开发的全局信封测试控制家庭错误率一样。开发了两个不同的自适应单阈值程序来实现这一目标。在一项广泛的模拟研究中研究了它们的性能。新方法由三个真实的数据示例说明。
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.
