Estimating the False Discovery Rate of Variable Selection
Methodology
2026-02-25 v4
Abstract
We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our method has a conservative (non-negative) bias in finite samples under standard statistical assumptions, and provide a bootstrap method for assessing its standard error. For methods like the Lasso, forward-stepwise regression, and the graphical Lasso, our estimator serves as a valuable companion to cross-validation, illuminating the tradeoff between prediction error and variable selection accuracy as a function of the model complexity parameter.
Cite
@article{arxiv.2408.07231,
title = {Estimating the False Discovery Rate of Variable Selection},
author = {Yixiang Luo and William Fithian and Lihua Lei},
journal= {arXiv preprint arXiv:2408.07231},
year = {2026}
}