Efficient Predictor Ranking and False Discovery Proportion Control in High-Dimensional Regression

TL;DR

This paper introduces a new ranking method based on the de-sparsified Lasso estimator for high-dimensional regression, enabling effective predictor prioritization and false discovery proportion control, especially in sparse models.

Contribution

It develops a novel ranking and variable selection procedure that asymptotically controls FDP using the de-sparsified Lasso, improving over existing methods in sparse settings.

Findings

Achieves optimal ranking of relevant predictors.

Consistently estimates FDP in high-dimensional models.

Outperforms existing methods in numerical simulations.

Abstract

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 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 numerical analyses, our procedure compares favorably to existing methods in ranking efficiency and FDP control when the regression model is relatively sparse.