2013/11/29 by Jian Huang, Shuangge Ma, Huang, Jian +6
Decision Sciences · Engineering · Mathematics · #62F99 #62J99 #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62F99 #msc:62J99 #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1311.7455
35 pages, 8 figures
arxiv created 2013/11/29 · openalex publication_date 2013/11/29 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new method, semi-penalized inference with direct false discovery rate control (SPIDR), for variable selection and confidence interval construction in high-dimensional linear regression. SPIDR first uses a semi-penalized approach to constructing estimators of the regression coefficients. We show that the SPIDR estimator is ideal in the sense that it equals an ideal least squares estimator with high probability under a sparsity and other suitable conditions. Consequently, the SPIDR estimator is asymptotically normal. Based on this distributional result, SPIDR determines the selection rule by directly controlling false discovery rate. This provides an explicit assessment of the selection error. This also 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 demonstrate its application on a breast cancer gene expression data set. Our simulation studies and data example suggest that SPIDR is a useful method for high-dimensional statistical inference in practice.