{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T07:39:52Z","timestamp":1785829192588,"version":"3.56.0"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,9,30]],"date-time":"2020-09-30T00:00:00Z","timestamp":1601424000000},"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":[[2021,5,15]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We propose the cyclic permutation test to test general linear hypotheses for linear models. The test is nonrandomized and valid in finite samples with exact Type I error $\\alpha$ for an arbitrary fixed design matrix and arbitrary exchangeable errors, whenever $1 \/ \\alpha$ is an integer and $n \/ p \\geqslant 1 \/ \\alpha - 1$, where $n$ is the sample size and $p$ is the number of parameters. The test involves applying the marginal rank test to $1 \/ \\alpha$ linear statistics of the outcome vector, where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a nonstandard cyclic permutation group under the null hypothesis. The power can be further enhanced by solving a secondary nonlinear travelling salesman problem, for which the genetic algorithm can find a reasonably good solution. Extensive simulation studies show that the cyclic permutation test has comparable power to existing tests. When testing for a single contrast of coefficients, an exact confidence interval can be obtained by inverting the test.<\/jats:p>","DOI":"10.1093\/biomet\/asaa079","type":"journal-article","created":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T19:22:34Z","timestamp":1600284154000},"page":"397-412","source":"Crossref","is-referenced-by-count":13,"title":["An assumption-free exact test for fixed-design linear models with exchangeable errors"],"prefix":"10.1093","volume":"108","author":[{"given":"Lihua","family":"Lei","sequence":"first","affiliation":[{"name":"Department of Statistics, Stanford University, 202 Sequoia Hall, 390 Serra Mall, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter J","family":"Bickel","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Berkeley, 367 Evans Hall, Berkeley, California 94720, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,9,30]]},"reference":[{"key":"2021051519492414000_B1","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1214\/aos\/1176344307","article-title":"Rank tests of sub-hypotheses in the general linear regression","volume":"6","author":"Adichie,","year":"1978","journal-title":"Ann. 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