标题： 关于硬币博弈在均值估计中的最优性 显示英文标题

标题： On the optimality of coin-betting for mean estimation

摘要： 我们考虑测试有界实随机变量均值的问题。 我们引入了e-变量和e-过程的最优类的概念，并确立了在基于e-变量的算法框架中，硬币博弈表述在测试和估计（条件）均值方面的最优性。 作为结果，我们提供了对此检验问题的所有有效e-变量和e-过程的直接且显式的表征。 在经典统计决策理论的语言中，我们完全描述了所有可接受的e-变量和e-过程的集合，并确定了相应的最小完备类。 显示英文摘要

摘要： We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based algorithmic frameworks for testing and estimating the (conditional) mean. As a consequence, we provide a direct and explicit characterisation of all valid e-variables and e-processes for this testing problem. In the language of classical statistical decision theory, we fully describe the set of all admissible e-variables and e-processes, and identify the corresponding minimal complete class.