Estimating means of bounded random variables by betting
该文提出新的置信区间和置信序列方法，用于估计有界均值，改进了经典Chernoff方法，在方差未知时自适应且性能优于现有方法，适用于有放回和无放回抽样。
Abstract 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.