Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach
Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach
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DOI：
10.1111/j.1467-9868.2004.00439.x
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发表时间：
2004-01-01
影响因子：
5.8
通讯作者：
Siegmund, D
中科院分区：
文献类型：
--
作者：
Storey, JD;Taylor, JE;Siegmund, D
错误发现率 (FDR) 是一个多重假设检验量，描述了所有被拒绝的原假设中假阳性结果的预期比例。 Benjamini 和 Hochberg 引入了这个量，并证明了特定的逐步提升 p 值方法可以控制 FDR。 Storey 引入了固定显着性区域的 FDR 点估计。前一种方法将 FDR 保守地控制在固定的预定水平，而后者为固定的预定显着性区域提供 FDR 的保守偏差估计。在这项工作中，我们在有限样本和渐近设置中表明，这两种方法的目标本质上是等效的。特别是，FDR 点估计可用于定义有效的 FDR 控制程序。在渐近设置中，我们还表明点估计可用于同时保守地估计所有显着性区域上的 FDR，这相当于同时控制所有级别的 FDR。我们使用的主要工具是将现有的 FDR 方法转化为涉及经验过程的程序。这简化了有限样本证明，提供了渐近结果的框架，并证明这些过程即使在某些形式的依赖下也是有效的。
The false discovery rate (FDR) is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses. Benjamini and Hochberg introduced this quantity and proved that a particular step-up p-value method controls the FDR. Storey introduced a point estimate of the FDR for fixed significance regions. The former approach conservatively controls the FDR at a fixed predetermined level, and the latter provides a conservatively biased estimate of the FDR for a fixed predetermined significance region. In this work, we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent. In particular, the FDR point estimates can be used to define valid FDR controlling procedures. In the asymptotic setting, we also show that the point estimates can be used to estimate the FDR conservatively over all significance regions simultaneously, which is equivalent to controlling the FDR at all levels simultaneously. The main tool that we use is to translate existing FDR methods into procedures involving empirical processes. This simplifies finite sample proofs, provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence.