On the Order-Conditional Optimality of Gaffke's Bound

arXiv:2607.22971 · math.ST, cs.LG, math.PR, stat.ML · Submitted 2026-07-25 · Read on arXiv

George Bissias, Erik Learned-Miller

math.ST, cs.LG, math.PR, stat.ML

Submitted: 2026-07-25

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Admissibility — 1× in this paper · explained in 2 episodes
• Exchangeability — 1× in this paper · explained in 2 episodes
• Monotonicity — 1× in this paper · explained in 2 episodes

Sources

• A New Confidence Interval for the Mean of a Bounded Random Variable
• On the admissibility of bounds on the mean of discrete, scalar probability distributions from an iid sample
• Algorithms for Approximating Conditionally Optimal Bounds
• Gaffke's confidence interval for the mean of bounded data is inadmissible but asymptotically efficient
• Towards Automated Confidence Bound Provers and Searchers
• An Exact Distribution-Free Test for Means of Nonnegative Random Variables

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