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We propose a new method, semi-penalized inference with direct false discoveryrate control (SPIDR), for variable selection and confidence intervalconstruction in high-dimensional linear regression. SPIDR first uses asemi-penalized approach to constructing estimators of the regressioncoefficients. We show that the SPIDR estimator is ideal in the sense that itequals an ideal least squares estimator with high probability under a sparsityand other suitable conditions. Consequently, the SPIDR estimator isasymptotically normal. Based on this distributional result, SPIDR determinesthe selection rule by directly controlling false discovery rate. This providesan explicit assessment of the selection error. This also naturally leads toconfidence intervals for the selected coefficients with a proper confidencestatement. We conduct simulation studies to evaluate its finite sampleperformance and demonstrate its application on a breast cancer gene expressiondata set. Our simulation studies and data example suggest that SPIDR is auseful method for high-dimensional statistical inference in practice.

Semi-Penalized Inference with Direct False Discovery Rate Control in High-Dimensions