Adaptive Selection for False Discovery Rate Control Leveraging Symmetry

Controlling the false discovery rate (FDR) in high-dimensional multiple testing has recently been advanced through mirror statistics via knockoff and data splitting. However, these approaches primarily emphasize the symmetry structure of the one-dimensional mirror statistics while inadvertently overlooking the distribution information from non-null features when determining the rejection region, potentially causing a power loss. To tackle this challenge, we present a novel framework termed symmetry-based adaptive selection (SAS), which leverages the symmetry property of the two-dimensional statistics associated with the null features to estimate the local FDR and thereby determine the rejection region. We provide theoretical evidence for the asymptotic validity of FDR control and emphasize the superior power performance of our proposed SAS. Extensive numerical results from both synthetic experiments and two real-world datasets demonstrate that the proposed SAS achieves satisfactory FDR control and significant power improvements over existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

近年来，高维多重检验中的错误发现率（False Discovery Rate, FDR）控制领域，通过柯克夫（knockoff）与数据拆分的镜像统计量方法取得了新进展。然而，此类方法主要聚焦于一维镜像统计量的对称结构，却在确定拒绝域时无意间忽略了非零特征（non-null features）的分布信息，可能导致检验功效损失。为解决这一难题，本文提出一种名为基于对称的自适应选择（Symmetry-based Adaptive Selection, SAS）的全新框架，该框架利用与零特征（null features）相关联的二维统计量的对称特性，对局部错误发现率（local FDR）进行估计，进而确定拒绝域。本文给出了FDR控制渐近有效性的理论依据，并论证了所提SAS方法的优异功效表现。通过合成实验与两个真实数据集的大量数值试验结果表明，所提SAS方法可实现良好的FDR控制效果，且相较于现有方法实现了显著的功效提升。本文的补充材料可在线获取，其中包含可用于复现研究工作的相关材料的标准化说明。