Bentkus-type asymptotic e-values

2026-06-04

AI Summary

This work addresses the conservativeness of existing asymptotic e-values, which stems from a so-called “missing factor” that degrades the accuracy of posterior inference and reduces power in multiple testing. For the first time, we incorporate Bentkus’s near-optimal concentration inequality into the construction of asymptotic e-values, thereby eliminating this missing factor and yielding substantially sharper statistical inference. Both theoretical analysis and empirical experiments demonstrate that the proposed method significantly outperforms current approaches: it produces tighter posterior credible intervals and achieves higher rejection rates in multiple hypothesis testing, effectively enhancing inferential precision and statistical power.

Abstract

Asymptotic e-values are emerging as a powerful alternative to asymptotic p-values, particularly in post-hoc inference and multiple testing, where significance levels may be data-dependent. Existing asymptotic e-values, however, suffer from the ``missing factor,'' a scaling inefficiency resulting in overly conservative inference. Drawing on the framework of near-optimal concentration inequalities developed by Bentkus in the 2000s, we introduce Bentkus-type asymptotic e-values and prove that they successfully eliminate the missing factor. We also demonstrate both theoretically and empirically that Bentkus-type e-values consistently deliver sharper inference than existing alternatives, leading to tighter post-hoc confidence intervals and higher rejection rates in multiple testing procedures.

Problem

• asymptotic e-values
• missing factor
• post-hoc inference
• multiple testing
• conservative inference

Innovation

• asymptotic e-values
• Bentkus inequality
• missing factor
• post-hoc inference
• multiple testing