{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T05:38:52Z","timestamp":1789105132226,"version":"build-2803163510"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T00:00:00Z","timestamp":1645660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,11,29]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen &amp; Qin (2010) is proposed. The asymptotic behaviour of the test statistic, as well as the randomized statistic, is studied under weak conditions. In our theoretical framework, observations are not assumed to be identically distributed even within groups. No condition on the eigenstructure of the covariance matrices is imposed. Furthermore, the sample sizes of the two groups are allowed to be unbalanced. Under general conditions, all possible asymptotic distributions of the test statistic are obtained. We derive the asymptotic level and local power of the approximate randomization test procedure. Our theoretical results show that the proposed test procedure can adapt to all possible asymptotic distributions of the test statistic, always has the correct test level asymptotically and has good power behaviour. Our numerical experiments show that the proposed test procedure has favourable performance compared with several alternative test procedures.<\/jats:p>","DOI":"10.1093\/biomet\/asac014","type":"journal-article","created":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T12:27:33Z","timestamp":1645532853000},"page":"1117-1132","source":"Crossref","is-referenced-by-count":19,"title":["An approximate randomization test for the high-dimensional two-sample Behrens\u2013Fisher problem under arbitrary covariances"],"prefix":"10.1093","volume":"109","author":[{"given":"Rui","family":"Wang","sequence":"first","affiliation":[{"name":"Center for Applied Statistics and School of Statistics, Renmin University of China , 59 Zhongguancun Street, Beijing 100872, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4983-9950","authenticated-orcid":false,"given":"Wangli","family":"Xu","sequence":"additional","affiliation":[{"name":"Center for Applied Statistics and School of Statistics, Renmin University of China , 59 Zhongguancun Street, Beijing 100872, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,2,24]]},"reference":[{"key":"2022112917594554900_B1","doi-asserted-by":"crossref","first-page":"6745","DOI":"10.1073\/pnas.96.12.6745","article-title":"Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays","volume":"96","author":"Alon,","year":"1999","journal-title":"Proc. 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