{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T02:01:28Z","timestamp":1789610488821,"version":"build-2803163510"},"reference-count":12,"publisher":"Oxford University Press (OUP)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints. Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic. We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints. If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion. Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.<\/jats:p>","DOI":"10.1093\/biomet\/asr002","type":"journal-article","created":{"date-parts":[[2011,4,23]],"date-time":"2011-04-23T20:24:24Z","timestamp":1303590264000},"page":"495-501","source":"Crossref","is-referenced-by-count":32,"title":["An Akaike-type information criterion for model selection under inequality constraints"],"prefix":"10.1093","volume":"98","author":[{"given":"R. M.","family":"Kuiper","sequence":"first","affiliation":[{"name":"Department of Methodology and Statistics, Utrecht University, PO Box 80140, 3508 TC, Utrecht, The Netherlands, r.m.kuiper@uu.nl, h.hoijtink@uu.nl"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Hoijtink","sequence":"additional","affiliation":[{"name":"Department of Methodology and Statistics, Utrecht University, PO Box 80140, 3508 TC, Utrecht, The Netherlands, r.m.kuiper@uu.nl, h.hoijtink@uu.nl"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. J.","family":"Silvapulle","sequence":"additional","affiliation":[{"name":"Department of Econometrics and Business Statistics, Monash University, Caulfield East, 3145, Australia, mervyn.silvapulle@monash.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2011,4,22]]},"reference":[{"key":"2020011011563571600_ASR002C1","first-page":"267","article-title":"Information theory and an extension of the maximum likelihood principle","volume-title":"Proc. 2nd Int. Symp. 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