Anytime-valid and asymptotically efficient inference driven by predictive recursion

• 成果类型: Article
• 署名作者: Dixit, Vaidehi; Martin, Ryan
• 署名单位: University of Missouri System; University of Missouri Columbia; North Carolina State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asae066
• 发表日期: 2025
• 关键词: maximum-likelihood-estimation; log-concave; Consistency; models

摘要

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.