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Optimal e-value testing for properly constrained hypotheses

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arxiv 2412.21125 v3 pith:32UG5DHV submitted 2024-12-30 math.ST stat.TH

Eugenio Clerico This is my paper · ORCID
classification math.STstat.TH
keywords e-variableshypothesisoptimalplayerresultsstrategytestingaddress
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Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective statistical test that rejects the null hypothesis as soon as sufficient evidence arises. Building on recent advances, we address the question of restricting the pool of e-variables to simplify strategy design without compromising effectiveness. We extend the results of Clerico(2024), by characterising optimal sets of e-variables for a broad class of non-parametric hypothesis tests, defined by finitely many regular constraints. As an application, we discuss this notion of optimality in algorithmic mean estimation, including for heavy-tailed random variables.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal e-values for testing the mean of a bounded random variable against a composite alternative

    math.ST 2026-01 accept novelty 8.0 of 10

    For bounded-mean testing without absolute continuity, GROW and REGROW optimal e-variables exist and are exactly coin-betting e-values Eα(x)=1+α(x−µ0), with α given by explicit formulas.

  2. Uniform mean estimation for monotonic processes

    math.ST 2025-02 conditional novelty 6.0 of 10

    Coin-betting plus a monotonicity-based continuous union bound yields uniform, anytime-valid, variance-adaptive confidence bands for monotonic mean functions such as CDFs.

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