Bentkus型渐近e值
Bentkus-type asymptotic e-values
AI总结：
针对现有渐近e值存在“缺失因子”导致推断保守的问题，基于Bentkus近最优集中不等式，提出Bentkus型渐近e值并证明其消除缺失因子，理论和实证表明其推断更锐利。
摘要：
渐近e值正在成为渐近p值的有力替代，特别是在事后推断和多重检验中，其中显著性水平可能依赖于数据。然而，现有的渐近e值存在“缺失因子”，这是一种缩放效率低下，导致过于保守的推断。借鉴Bentkus在2000年代发展的近最优集中不等式框架，我们引入了Bentkus型渐近e值，并证明它们成功消除了缺失因子。我们还从理论和实证上证明，Bentkus型e值始终比现有替代方案提供更锐利的推断，从而在事后置信区间和多重检验程序中实现更紧的置信区间和更高的拒绝率。
英文摘要：
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.
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