Bentkus-type asymptotic e-values
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.
Related
- Regular closed gradient ranges and asymptotic gradient values
- Asymptotic Theory for Combining Dependent p-Values for Global Hypothesis Testing
- Asymptotic equivalence and exact values for second-order Zarankiewicz numbers
- On Asymptotic Outlier Rejection in Bayesian Mixed Poisson Regression Models Under Extreme Target and Covariate Values
- New Hoffman-type generators for alternating multiple zeta values
BibTeX
@misc{martineztaboada2026bentkustype,
title = {{Bentkus-type asymptotic e-values}},
author = {Diego Martinez-Taboada and Ben Chugg and Aaditya Ramdas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.06332},
eprint = {2606.06332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.06332},
}
RIS
TY - UNPB
TI - Bentkus-type asymptotic e-values
AU - Diego Martinez-Taboada
AU - Ben Chugg
AU - Aaditya Ramdas
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2606.06332
UR - https://arxiv.org/abs/2606.06332
AB - 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.
ER -