{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:33:13Z","timestamp":1790037193749,"version":"4.0.1"},"reference-count":53,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We consider testing invariance of a distribution under an algebraic group of transformations, such as permutations or sign flips. As such groups are typically huge, tests based on the full group are often computationally infeasible. Hence, it is standard practice to use a random subset of transformations. We improve upon this by replacing the random subset with a strategically chosen, fixed subgroup of transformations. In a generalized location model, we show that the resulting tests are often consistent for lower signal-to-noise ratios. Moreover, we establish an analogy between the power improvement and switching from a t-test to a Z-test under normality. Importantly, in permutation-based multiple testing, the efficiency gain with our approach can be huge, since we attain the same power with many fewer permutations.<\/jats:p>","DOI":"10.1093\/biomet\/asad050","type":"journal-article","created":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T15:54:53Z","timestamp":1693583693000},"page":"441-458","source":"Crossref","is-referenced-by-count":8,"title":["More efficient exact group invariance testing: using a representative subgroup"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3784-4480","authenticated-orcid":false,"given":"N W","family":"Koning","sequence":"first","affiliation":[{"name":"Econometric Institute, Erasmus University Rotterdam , PO Box 1738, 3000 DR Rotterdam, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J","family":"Hemerik","sequence":"additional","affiliation":[{"name":"Department Biometris, Wageningen University & Research , PO Box 16, 6700 AC Wageningen, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,9,1]]},"reference":[{"key":"2024051307572498500_asad050-B1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1111\/1467-842X.00156","article-title":"Permutation tests for linear models","volume":"43","author":"Anderson","year":"2001","journal-title":"Aust.New Zeal. 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