A Scale-Free Approach for False Discovery Rate Control in Generalized Linear Models

The Generalized Linear Model (GLM) has been widely used in practice to model counts or other types of non-Gaussian data. This article introduces a framework for feature selection in the GLM that can achieve robust False Discovery Rate (FDR) control. The main idea is to construct a mirror statistic based on data perturbation to measure the importance of each feature. FDR control is achieved by taking advantage of the mirror statistic’s property that its sampling distribution is (asymptotically) symmetric about zero for any null feature. In the moderate-dimensional setting, that is, p/n→κ∈(0,1), we construct the mirror statistic based on the maximum likelihood estimation. In the high-dimensional setting, that is, p≫n, we use the debiased Lasso to build the mirror statistic. The proposed methodology is scale-free as it only hinges on the symmetry of the mirror statistic, thus, can be more robust in finite-sample cases compared to existing methods. Both simulation results and a real data application show that the proposed methods are capable of controlling the FDR and are often more powerful than existing methods including the Benjamini-Hochberg procedure and the knockoff filter. Supplementary materials for this article are available online.