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Simultaneously finding multiple influential variables and controlling thefalse discovery rate (FDR) for linear regression models is a fundamentalproblem. We here propose the Gaussian Mirror (GM) method, which creates foreach predictor variable a pair of mirror variables by adding and subtracting arandomly generated Gaussian perturbation, and proceeds with a certainregression method, such as the ordinary least-square or the Lasso (the mirrorvariables can also be created after selection). The mirror variables naturallylead to test statistics effective for controlling the FDR. Under a mildassumption on the dependence among the covariates, we show that the FDR can becontrolled at any designated level asymptotically. We also demonstrate throughextensive numerical studies that the GM method is more powerful than manyexisting methods for selecting relevant variables subject to FDR control,especially for cases when the covariates are highly correlated and theinfluential variables are not overly sparse.

Controlling False Discovery Rate Using Gaussian Mirrors