{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T18:01:47Z","timestamp":1782324107099,"version":"3.54.5"},"reference-count":90,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T00:00:00Z","timestamp":1682035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100008398","name":"VILLUM FONDEN","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008398","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002808","name":"Carlsberg Foundation","doi-asserted-by":"publisher","award":["0069071"],"award-info":[{"award-number":["0069071"]}],"id":[{"id":"10.13039\/501100002808","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009708","name":"Novo Nordisk Fonden","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009708","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce statistical testing under distributional shifts. We are interested in the hypothesis P*\u2208H0 for a target distribution P*, but observe data from a different distribution Q*. We assume that P* is related to Q* through a known shift \u03c4 and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (similarly to sampling importance resampling) and then applies an existing test in the target domain. We prove that if the size of the resample is of order o(n) and the resampling weights are well behaved, this procedure inherits the pointwise asymptotic level and power from the target test. If the map \u03c4 is estimated from data, we maintain the above guarantees under mild conditions on the estimation. Our results extend to finite sample level, uniform asymptotic level, a different resampling scheme, and statistical inference different from testing. Testing under distributional shifts allows us to tackle a diverse set of problems. We argue that it may prove useful in contextual bandit problems and covariate shift, show how it reduces conditional to unconditional independence testing and provide example applications in causal inference.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad018","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T20:28:32Z","timestamp":1682108912000},"page":"597-663","source":"Crossref","is-referenced-by-count":6,"title":["Statistical testing under distributional shifts"],"prefix":"10.1093","volume":"85","author":[{"given":"Nikolaj","family":"Thams","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen , Copenhagen , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sorawit","family":"Saengkyongam","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen , Copenhagen , 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