Abstract

We propose a semi-penalized inference approach with direct false discovery rate control for variable selection and confidence interval construction in high-dimensional linear regression. With this approach, we first calculate semi-penalized estimators of the regression coefficients, which are shown to be asymptotically normal under a sparsity condition and other appropriate conditions. We then carry out selection by controlling the false discovery rate based on the distributions of these estimators. The approach provides an explicit assessment of the selection error and naturally leads to confidence intervals for the selected coefficients with a proper confidence statement. We conduct simulation studies to evaluate its finite sample performance and illustrate its application on a breast cancer gene expression data set. Our simulation studies and data example demonstrate that SPIDR is a useful method for high-dimensional statistical inference in practice.