E-STATISTICS, GROUP INVARIANCE AND ANYTIME-VALID TESTING
成果类型：
Article
署名作者：
Perez-Ortiz, Muriel Felipe; Lardy, Tyron; Heide, Rianne; Gruenwald, Peter D.
署名单位：
Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University; Vrije Universiteit Amsterdam
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/24-AOS2394
发表日期：
2024
页码：
1410-1432
关键词：
摘要：
We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant statistic. We show that among all e-statistics, invariant or not, the likelihood ratio of the maximally invariant statistic is GROW, both in the absolute and in the relative sense, and that an anytime-valid test can be based on it. The GROW e-statistic is equal to a Bayes factor with a right Haar prior on G. Our treatment avoids nonuniqueness issues that sometimes arise for such priors in Bayesian contexts. A crucial assumption on the group G is its amenability, a well-known group-theoretical condition, which holds, for instance, in scale-location families. Our results also apply to finitedimensional linear regression.
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