Controlling False Discovery Rate Using Gaussian Mirrors
Controlling False Discovery Rate Using Gaussian Mirrors
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DOI：
10.1080/01621459.2021.1923510
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发表时间：
2019-11
影响因子：
3.7
通讯作者：
Xin Xing;Zhigen Zhao;Jun S. Liu
中科院分区：
文献类型：
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作者：
Xin Xing;Zhigen Zhao;Jun S. Liu
同时发现多个影响变量并控制线性回归模型的误发现率(FDR)是一个基本问题。这里我们提出了高斯镜(GM)方法，它通过增加和减少随机产生的高斯扰动来为每个预测变量创建一对镜像变量，并进行某种回归方法，如普通的最小二乘法或套索(镜像变量也可以在选择后创建)。镜像变量自然会导致有效控制FDR的测试统计数据。在较温和的协变量相关性假设下，我们证明了FDR可以渐近控制在任意指定的水平。我们还通过大量的数值研究表明，GM方法在选择受FDR控制的相关变量方面比现有的许多方法更有效，特别是在协变量高度相关且影响变量不是太稀疏的情况下。
Abstract Simultaneously, finding multiple influential variables and controlling the false discovery rate (FDR) for linear regression models is a fundamental problem. We here propose the Gaussian Mirror (GM) method, which creates for each predictor variable a pair of mirror variables by adding and subtracting a randomly generated Gaussian perturbation, and proceeds with a certain regression method, such as the ordinary least-square or the Lasso (the mirror variables can also be created after selection). The mirror variables naturally lead to test statistics effective for controlling the FDR. Under a mild assumption on the dependence among the covariates, we show that the FDR can be controlled at any designated level asymptotically. We also demonstrate through extensive numerical studies that the GM method is more powerful than many existing methods for selecting relevant variables subject to FDR control, especially for cases when the covariates are highly correlated and the influential variables are not overly sparse.