We build a valid p-value based on a concentration inequality for bounded random variables introduced by Pelekis, Ramon and Wang. The motivation behind this work is the calibration of predictive algorithms in a distribution-free setting. The super-uniform p-value is tighter than Hoeffding and Bentkus alternatives in certain regions. Even though we are motivated by a calibration setting in a machine learning context, the ideas presented in this work are also relevant in classical statistical inference. Furthermore, we compare the power of a collection of valid p- values for bounded losses, which are presented in previous literature.

翻译：基于Pelekis、Ramon和Wang提出的有界随机变量浓度不等式，我们构建了一个有效p值。本研究的动机是在无分布假设下对预测算法进行校准。该超均匀p值在某些区间内比Hoeffding和Bentkus替代方法更严格。尽管我们以机器学习背景下的校准场景为出发点，但本文提出的思想同样适用于经典统计推断。此外，我们比较了先前文献中针对有界损失函数的一系列有效p值的统计功效。