{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T18:15:59Z","timestamp":1772907359479,"version":"3.50.1"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,8,14]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate analysis of variance, and the nonparametric one-way multivariate analysis of variance in high dimensions. To implement the test procedure, we introduce a sample-splitting-based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings.<\/jats:p>","DOI":"10.1093\/biomet\/asad001","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T13:10:06Z","timestamp":1674047406000},"page":"777-797","source":"Crossref","is-referenced-by-count":3,"title":["High-dimensional analysis of variance in multivariate linear regression"],"prefix":"10.1093","volume":"110","author":[{"given":"Zhipeng","family":"Lou","sequence":"first","affiliation":[{"name":"Princeton University Department of Operations Research and Financial Engineering, , Sherrerd Hall, Charlton Street, Princeton, New Jersey 08544, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianyang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Texas A&M University Department of Statistics, , Blocker 435, College Station, Texas 77843, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei Biao","family":"Wu","sequence":"additional","affiliation":[{"name":"University of Chicago Department of Statistics, , 5734 S. 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