摘要：We consider the problem of variable selection in high-dimensional statistical models where the goal is to report a set of variables, out of many predictors $X_{1},\dotsc ,X_{p}$, that are relevant to a response of interest. For linear high-dimensional model, where the number of parameters exceeds the number of samples $(p>n)$, we propose a procedure for variables selection and prove that it controls the directional false discovery rate (FDR) below a pre-assigned significance level $q\in [0,1]$. We further analyze the statistical power of our framework and show that for designs with subgaussian rows and a common precision matrix $\Omega \in{\mathbb{R}} ^{p\times p}$, if the minimum nonzero parameter $\theta_{\min }$ satisfies \[\sqrt{n}\theta_{\min }-\sigma \sqrt{2(\max_{i\in [p]}\Omega_{ii})\log \left(\frac{2p}{qs_{0}}\right)}\to \infty \,,\] then this procedure achieves asymptotic power one.
