Proposer of the vote of thanks to Waudy-Smith and Ramdas and contribution to the Discussion of ‘Estimating means of bounded random variables by betting’
本文提出了估计有界随机变量均值的置信区间和置信序列，改进了Chernoff方法，通过新的复合非负鞅和Ville极大不等式，在抽样有放回和无放回下均优于现有方法。
We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean.Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form "betting" CSs and CIs.Our method combines new composite nonnegative (super) martingales with Ville's maximal inequality, with strong connections to testing by betting and the method of mixtures.We also show how these ideas can be extended to sampling without replacement.In all cases, our bounds are adaptive to the unknown variance, and empirically vastly outperform prior approaches, establishing a new state-of-the-art for four fundamental problems: CSs and CIs for bounded means, when sampling with and without replacement.