Controlling False Discovery Rate Using Gaussian Mirrors
提出高斯镜像方法，通过为每个预测变量添加随机高斯扰动生成镜像变量，结合最小二乘或Lasso等回归方法，在控制错误发现率的同时有效识别重要变量，尤其适用于协变量高度相关且重要变量不稀疏的场景。
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.