mlsanityData to 7 Oct 2026

Estimating means of bounded random variables by betting

arXiv 2010.09686 ↗First posted 19 Oct 2020math.ST stat.ME stat.MLcited by 164

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Abstract (arXiv)

This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that can be seen as a generalization and improvement of the celebrated Chernoff method. At its heart, it is based on a class of composite nonnegative martingales, with strong connections to testing by betting and the method of mixtures. We show how to extend these ideas to sampling without replacement, another heavily studied problem. In all cases, our bounds are adaptive to the unknown variance, and empirically vastly outperform existing approaches based on Hoeffding or empirical Bernstein inequalities and their recent supermartingale generalizations. In short, we establish a new state-of-the-art for four fundamental problems: CSs and CIs for bounded means, when sampling with and without replacement.

Key facts. Cited by 164 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Oct 2020.

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Citing papers per year: 2021: 7; 2022: 13; 2023: 21; 2024: 22; 2025: 34; 2026: 67.

164 papers.

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