Bentkus-type asymptotic e-values

Diego Martinez-Taboada; Ben Chugg; Aaditya Ramdas

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arXiv · 2606.06332

Bentkus-type asymptotic e-values

Diego Martinez-Taboada·Ben Chugg·Aaditya Ramdas

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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.

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BibTeX RIS

Diego Martinez-Taboada, Ben Chugg, Aaditya Ramdas. 2026-06-04. Bentkus-type asymptotic e-values. https://arxiv.org/abs/2606.06332

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