{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T21:41:05Z","timestamp":1793396465681,"version":"4.5.0"},"reference-count":41,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T00:00:00Z","timestamp":1715731200000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100010663","name":"European Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform Type-I error control and derive explicit bounds on the finite-sample performance of the test. We demonstrate the empirical performance of the procedure in comparison to existing sequential and nonsequential independence tests. Furthermore, since the proposed test is distribution-free under the null hypothesis, we empirically simulate the gap due to Ville\u2019s inequality, the supermartingale analogue of Markov\u2019s inequality, that is commonly applied to control Type-I error in anytime-valid inference, and apply this to construct a truncated sequential test.<\/jats:p>","DOI":"10.1093\/biomet\/asae023","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T16:15:48Z","timestamp":1715616948000},"page":"1169-1186","source":"Crossref","is-referenced-by-count":7,"title":["A rank-based sequential test of independence"],"prefix":"10.1093","volume":"111","author":[{"given":"Alexander","family":"Henzi","sequence":"first","affiliation":[{"name":"Seminar for Statistics, ETH Z\u00fcrich , R\u00e4mistrasse 101 , 8092 Z\u00fcrich,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Law","sequence":"additional","affiliation":[{"name":"Seminar for Statistics, ETH Z\u00fcrich , R\u00e4mistrasse 101 , 8092 Z\u00fcrich,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"key":"2025051320021402500_asae023-B1","first-page":"42","volume-title":"Proc. 32nd Conf. 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