Estimating the False Discovery Rate of Variable Selection

TL;DR

This paper presents a universal estimator for the false discovery rate in variable selection, applicable across various statistical models, and offers methods to evaluate its bias and standard error.

Contribution

It introduces a new estimator for false discovery rate applicable to multiple model selection procedures, with theoretical bias guarantees and bootstrap-based error assessment.

Findings

Estimator is conservative with non-negative bias under standard assumptions.

Provides a bootstrap method for standard error estimation.

Helps balance prediction accuracy and variable selection in practice.

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.