{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,26]],"date-time":"2026-10-26T22:38:52Z","timestamp":1793054332861,"version":"4.5.0"},"reference-count":46,"publisher":"Institute of Mathematical Statistics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2024,8,1]]},"abstract":"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.<\/jats:p>","DOI":"10.1214\/24-aos2394","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T01:48:38Z","timestamp":1728006518000},"page":"1410-1432","source":"Crossref","is-referenced-by-count":18,"title":["E-statistics, group invariance and anytime-valid testing"],"prefix":"10.1214","volume":"52","author":[{"given":"Muriel Felipe","family":"P\u00e9rez-Ortiz","sequence":"first","affiliation":[{"name":"Statistics, Probability and Operations Research Cluster, Eindhoven University of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tyron","family":"Lardy","sequence":"additional","affiliation":[{"name":"Mathematical Institute, Leiden University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rianne","family":"de Heide","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vrije Universiteit"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter D.","family":"Gr\u00fcnwald","sequence":"additional","affiliation":[{"name":"Centrum Wiskunde & Informatica"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"23","doi-asserted-by":"publisher","unstructured":"Kullback, S.<\/small> and Leibler, R. 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