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.

翻译：渐近e值正逐渐成为渐近p值的有力替代，尤其是在显著性水平可能依赖于数据的后验推断与多重检验中。然而，现有渐近e值存在“缺失因子”问题，即缩放效率不足导致推断过于保守。本文借鉴本特库斯（Bentkus）在21世纪初发展的近最优集中不等式框架，提出本特库斯型渐近e值，并证明其成功消除了缺失因子。我们还从理论与实证两方面证明，本特库斯型e值始终能比现有替代方法提供更精确的推断，从而在后验置信区间与多重检验程序中实现更紧的置信区间与更高的拒绝率。