Multiple Testing in Generalized Universal Inference

TL;DR

This paper introduces a distribution-free method for multiple hypothesis testing using generalized universal inference and e-values, ensuring valid error control without distributional assumptions, demonstrated through simulations in quantile regression.

Contribution

It combines generalized universal inference with the e-BH procedure to control error rates in multiple testing without relying on distributional assumptions.

Findings

Valid error control demonstrated in simulations

Method maintains power in multiple testing scenarios

Applicable to risk minimization problems like quantile regression

Abstract

Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to properly correct for multiplicity. Standard e-value constructions, however, require distributional assumptions that may not be justifiable. This paper demonstrates that the generalized universal inference framework can be used along with the e-BH procedure to control frequentist error rates in multiple testing when the quantities of interest are minimizers of risk functions, thereby avoiding the need for distributional assumptions. We demonstrate the validity and power of this approach via a simulation study, testing the significance of a predictor in quantile regression.