Efficient Predictor Ranking and False Discovery Proportion Control in High-Dimensional Regression
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We propose a ranking and selection procedure to prioritize relevant predictors and control false discovery proportion (FDP) of 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 consistency. Further, we study the potential advantage of the new method over the Lasso solution path for predictor ranking. 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 simulation analyses, our procedure compares favorably to existing methods in ranking efficiency and FDP control. An application to genetic association study demonstrates improved power of the procedure.
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