Anytime-valid and asymptotically efficient inference driven by predictive recursion
提出一种基于预测递归算法的e过程构造方法，用于区分两个模型，能在未知停止规则下实现随时有效的推断，且渐近效率达到一阶最优。
Summary Distinguishing two 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 algorithm originally designed to recursively fit nonparametric mixture models. The resulting predictive recursion $ e $-process affords anytime-valid inference and is asymptotically efficient in the sense that its growth rate is first-order optimal relative to the predictive recursion’s mixture model.