{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:30:15Z","timestamp":1753889415631,"version":"3.37.0"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":6465,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>This paper gives simple nonuniform bounds on the tail areas of the permutation distribution of the usual Student's<jats:italic>t<\/jats:italic>-statistic when the observations are independent with symmetric distributions. As opposed to uniform bounds, nonuniform bounds depend on the observed sample. It is shown that the nonuniform bounds proposed are always tighter than uniform exponential bounds previously suggested. The use of the bounds to perform nonparametric<jats:italic>t<\/jats:italic>-tests is discussed and numerical examples are presented. Further, the bounds are extended to<jats:italic>t<\/jats:italic>-tests in the context of a simple linear regression.<\/jats:p>","DOI":"10.1017\/s0266466600004448","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:45:16Z","timestamp":1236699916000},"page":"253-263","source":"Crossref","is-referenced-by-count":10,"title":["Nonuniform Bounds for Nonparametric<i>t<\/i>-Tests"],"prefix":"10.1017","volume":"7","author":[{"given":"Jean-Marie","family":"Dufour","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc","family":"Hallin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"volume-title":"Introduction to Mathematical Probability","year":"1937","author":"Uspenky","key":"S0266466600004448_ref021"},{"key":"S0266466600004448_ref020","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/j.2517-6161.1982.tb01191.x","article-title":"Saddlepoint approximations for permutation tests and confidence intervals","author":"Robinson","year":"1982","journal-title":"Journal of the Royal Statistical Society, Series B 44"},{"key":"S0266466600004448_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5931-2"},{"key":"S0266466600004448_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177730089"},{"key":"S0266466600004448_ref016","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1963.10500830"},{"key":"S0266466600004448_ref015","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729436"},{"key":"S0266466600004448_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3932(80)90001-X"},{"volume-title":"The Design of Experiments","year":"1935","author":"Fisher","key":"S0266466600004448_ref011"},{"key":"S0266466600004448_ref010","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/73.1.242"},{"key":"S0266466600004448_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/2938212"},{"key":"S0266466600004448_ref007","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-842X.1980.tb01161.x"},{"key":"S0266466600004448_ref006","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177732803"},{"volume-title":"Theory of Probability","year":"1927","author":"Bernstein","key":"S0266466600004448_ref005"},{"key":"S0266466600004448_ref003","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1962.10482149"},{"key":"S0266466600004448_ref002","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1983.10478024"},{"key":"S0266466600004448_ref001","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343350"},{"volume-title":"Nonparametric Methods in Statistics","year":"1957","author":"Fraser","key":"S0266466600004448_ref012"},{"key":"S0266466600004448_ref004","first-page":"38","article-title":"Sur une modification de l'in\u00e9galit\u00e9 de Tchebichef","volume":"I","author":"Bernstein","year":"1924","journal-title":"Ann. 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