论文标题
通过投注来估计有限随机变量的平均值
Estimating means of bounded random variables by betting
论文作者
论文摘要
本文衍生了置信区间（CI）和时间统一的置信序列（CS），以估算有界观测值的未知平均值的经典问题。我们提出了一种推导浓度界限的一般方法，可以看作是著名的切尔诺夫方法的概括和改进。它的核心是基于一类复合非负胸腔，通过投注和混合物方法与测试有很强的联系。我们展示了如何将这些想法扩展到无需更换的情况下，这是另一个经过深入研究的问题。在所有情况下，我们的界限都适应未知的差异，并且基于Hoffding或经验的Bernstein不平等及其最近的Supermartingale概括，经验上大大优于现有方法。简而言之，我们为四个基本问题建立了一个新的最先进的问题：当或不替换时采样时，CSS和CI进行有限的手段。
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.
