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We construct a constrained estimator of the parameter vector and develop asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. We conduct a simulation study to examine the finite sample performance of our estimator and tests. Furthermore, we propose a coefficient of determination for the GIA-CR model. As a separate contribution, we establish the asymptotic distribution of the constrained estimator in Blanco-Fern\u00e1ndez (2015, Multiple Set Arithmetic-Based Linear Regression Models for Interval-Valued Variables) in which the parameters satisfy an increasing number of random inequality constraints.<\/jats:p>","DOI":"10.1017\/s0266466621000360","type":"journal-article","created":{"date-parts":[[2021,8,13]],"date-time":"2021-08-13T09:58:12Z","timestamp":1628848692000},"page":"27-69","source":"Crossref","is-referenced-by-count":2,"title":["UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL"],"prefix":"10.1017","volume":"39","author":[{"given":"Yanqin","family":"Fan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuetao","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,8,13]]},"reference":[{"key":"S0266466621000360_r56","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2009.08.010"},{"key":"S0266466621000360_r13","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2011.03.005"},{"key":"S0266466621000360_r52","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-80350-5_43"},{"key":"S0266466621000360_r70","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478499"},{"key":"S0266466621000360_r49","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1976.10481560"},{"key":"S0266466621000360_r16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2015.07.003"},{"key":"S0266466621000360_r35","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-008-9135-5"},{"key":"S0266466621000360_r58","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-57984-4_9"},{"key":"S0266466621000360_r57","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijid.2020.02.060"},{"key":"S0266466621000360_r40","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2008.02.007"},{"key":"S0266466621000360_r36","first-page":"205","article-title":"Integration des applications mesurables dont la valeur est un compact convexe","volume":"10","author":"Hukuhara","year":"1967","journal-title":"Funkcialaj Ekvacioj"},{"key":"S0266466621000360_r48","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1993.tb04028.x"},{"key":"S0266466621000360_r55","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.05.003"},{"key":"S0266466621000360_r18","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdq020"},{"key":"S0266466621000360_r10","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1080\/01621459.1994.10476836","article-title":"P values maximized over a confidence set for the nuisance parameter","volume":"89","author":"Berger","year":"1994","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466621000360_r15","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.3982\/ECTA7637","article-title":"Set identified linear models","volume":"80","author":"Bontemps","year":"2012","journal-title":"Econometrica"},{"key":"S0266466621000360_r63","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1015951997"},{"key":"S0266466621000360_r65","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476739"},{"key":"S0266466621000360_r4","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466613000315"},{"key":"S0266466621000360_r59","doi-asserted-by":"publisher","DOI":"10.1287\/moor.20.4.769"},{"key":"S0266466621000360_r33","doi-asserted-by":"publisher","DOI":"10.2307\/1912529"},{"key":"S0266466621000360_r68","volume-title":"Asymptotic Statistics","author":"Van\u00a0der Vaart","year":"2000"},{"key":"S0266466621000360_r69","doi-asserted-by":"publisher","DOI":"10.1093\/aje\/152.3.247"},{"key":"S0266466621000360_r42","unstructured":"Knight, K. 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