mlsanityData to 7 Oct 2026

Bentkus-type asymptotic e-values

arXiv 2606.06332 ↗First posted 4 Jun 2026math.ST stat.ME stat.MLcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 4 Jun 2026.

Builds on

22 of 45 references.

References · 22

  1. 2018Time-uniform, nonparametric, nonasymptotic confidence sequencescited by 220
  2. 2020Estimating means of bounded random variables by bettingcited by 164
  3. 2019Safe Testingcited by 98
  4. 2024Hypothesis testing with e-valuescited by 70
  5. 2019Universal Inferencecited by 43
  6. 2025E-Values Expand the Scope of Conformal Predictioncited by 23
  7. 2022Catoni-style confidence sequences for heavy-tailed mean estimationcited by 17
  8. 2022Post-selection inference for e-value based confidence intervalscited by 14
  9. 2022Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alphacited by 14
  10. 2022Principal-Agent Hypothesis Testingcited by 13
  11. 2024Mean Estimation in Banach Spaces Under Infinite Variance and Martingale Dependencecited by 5
  12. 2025Vector-valued self-normalized concentration inequalities beyond sub-Gaussianitycited by 4
10 more
  1. 2024Asymptotic and compound e-values: multiple testing and empirical Bayescited by 3
  2. 2025On admissibility in post-hoc hypothesis testingcited by 3
  3. 2025Rao-Blackwellized e-variablescited by 3
  4. 2013An optimal three-way stable and monotonic spectrum of bounds on quantiles: a spectrum of coherent measures of financial risk and economic inequalitycited by 2
  5. 2024Optimal E-Values for Exponential Families: the Simple Casecited by 2
  6. 2024Admissible online closed testing must employ e-valuescited by 2
  7. 2025Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testingcited by 2
  8. 2026Post-Hoc Large-Sample Statistical Inferencecited by 2
  9. 2026Equivalence testing with data-dependent and post-hoc equivalence marginscited by 2
  10. 2024E-Values for Exponential Families: the General Casecited by 1

Built on by

Not cited yet.