Adaptive FDR control under independence and dependence
Adaptive FDR control under independence and dependence
复制标题
DOI：
--
复制
发表时间：
2007-07
期刊：
影响因子：
--
通讯作者：
G. Blanchard;Étienne Roquain
中科院分区：
文献类型：
--
作者：
G. Blanchard;Étienne Roquain
在多个假设检验的背景下，要检验的假设池中真实零假设的比例$\pi_0$通常起着至关重要的作用，尽管它通常是先验未知的。为了提高效率而使用该量的隐式或显式估计的测试过程称为自适应。在本文中，我们专注于错误发现率（FDR）的控制问题，我们提出了新的自适应多测试程序与FDR的控制。首先，在假设独立的p$值的情况下，我们提出了两个新的程序，并给出了一个统一的审查其他现有的自适应程序，已证明控制FDR。我们报告了大量的模拟结果比较这些程序和测试其鲁棒性时，违反独立性假设。拟议的新程序似乎与现有程序具有竞争力。不过，据报道，总体上最好的是Storey的估计量，但参数设置似乎以前没有考虑过。其次，我们提出了自适应版本的升压程序，已证明控制FDR下的正依赖性和未指定的依赖性的$p$值，分别。虽然模拟只显示在有限的情况下，非自适应程序的改进，这些是我们的知识之间的第一个理论上成立的自适应多个测试程序，控制FDR时，$p$-值是不独立的。
In the context of multiple hypotheses testing, the proportion $\pi_0$ of true null hypotheses in the pool of hypotheses to test often plays a crucial role, although it is generally unknown a priori. A testing procedure using an implicit or explicit estimate of this quantity in order to improve its efficency is called adaptive. In this paper, we focus on the issue of False Discovery Rate (FDR) control and we present new adaptive multiple testing procedures with control of the FDR. First, in the context of assuming independent $p$-values, we present two new procedures and give a unified review of other existing adaptive procedures that have provably controlled FDR. We report extensive simulation results comparing these procedures and testing their robustness when the independence assumption is violated. The new proposed procedures appear competitive with existing ones. The overall best, though, is reported to be Storey's estimator, but for a parameter setting that does not appear to have been considered before. Second, we propose adaptive versions of step-up procedures that have provably controlled FDR under positive dependences and unspecified dependences of the $p$-values, respectively. While simulations only show an improvement over non-adaptive procedures in limited situations, these are to our knowledge among the first theoretically founded adaptive multiple testing procedures that control the FDR when the $p$-values are not independent.