2022/08/16 by Pérez-Ortiz, Muriel Felipe, Lardy, Tyron, de Heide, Rianne +1 · 3 citations
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2208.07610
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 finite-dimensional linear regression.