Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the stopping rule that determines the data collection process is not available. This paper proposes an e-process construction based on the predictive recursion (PR) algorithm originally designed to recursively fit nonparametric mixture models. The resulting PRe-process affords anytime valid inference and is asymptotically efficient in the sense that its growth rate is first-order optimal relative to PR's mixture model.

翻译：区分两个候选模型是一个基础且具有重要实际意义的统计问题。错误率控制对检验逻辑至关重要，但在复杂的非参数设定下，尤其是在决定数据收集过程的停止规则未知时，这一目标往往难以实现。本文提出了一种基于预测递归（PR）算法的e-过程构造方法，该算法最初设计用于递归拟合非参数混合模型。由此得到的PRe-过程能够提供任意时间有效的推断，并且在渐近意义下具有最优性：其相对于PR混合模型的增长率是一阶最优的。