Predictor ranking and false discovery proportion control in high-dimensional regression

X. Jessie Jeng and Xiongzhi Chen

Journal of Multivariate Analysis, 2019, vol. 171, issue C, 163-175

Abstract: We propose a ranking and selection procedure to prioritize relevant predictors and control false discovery proportion (FDP) in variable selection. Our procedure utilizes a new ranking method built upon the de-sparsified Lasso estimator. We show that the new ranking method achieves the optimal order of minimum non-zero effects in ranking relevant predictors ahead of irrelevant ones. Adopting the new ranking method, we develop a variable selection procedure to asymptotically control FDP at a user-specified level. We show that our procedure can consistently estimate the FDP of variable selection as long as the de-sparsified Lasso estimator is asymptotically normal. In simulations, our procedure compares favorably to existing methods in ranking efficiency and FDP control when the regression model is relatively sparse.

Keywords: Multiple testing; Penalized regression; Sparsity; Variable selection (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:171:y:2019:i:c:p:163-175

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DOI: 10.1016/j.jmva.2018.12.006

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