{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T08:29:13Z","timestamp":1791448153940,"version":"4.3.3"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":2490,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1150435"],"award-info":[{"award-number":["DMS-1150435"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"American Statistical Association\u2013National Science Foundation\u2013Bureau of Labor Statistics fellowship programme"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,3,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non-parametric double-cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of the test increases to 1 as the sample size increases, under very mild assumptions\u2014even when the alternative is misspecified, i.e. the power of the test converges to 1 for any true regression function that deviates (in a non-degenerate way) from the parametric null hypothesis. We also formulate tests for the linear versus partial linear model and consider the special case of the additive model. Simulations show that our procedure behaves well consistently when compared with other methods. Although the alternative fit is non-parametric, no tuning parameters are involved. Supplementary materials with proofs and technical details are available on line.<\/jats:p>","DOI":"10.1111\/rssb.12178","type":"journal-article","created":{"date-parts":[[2016,4,25]],"date-time":"2016-04-25T03:52:40Z","timestamp":1461556360000},"page":"423-448","source":"Crossref","is-referenced-by-count":11,"title":["Testing Against a Linear Regression Model Using Ideas from Shape-Restricted Estimation"],"prefix":"10.1093","volume":"79","author":[{"given":"Bodhisattva","family":"Sen","sequence":"first","affiliation":[{"name":"Columbia University , New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mary","family":"Meyer","sequence":"additional","affiliation":[{"name":"Colorado State University , Fort Collins , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,4,24]]},"reference":[{"key":"2023021801103382700_rssb12178-cit-0001","first-page":"5710","volume-title":"A parallel method for large scale convex regression problems","author":"Aybat","year":"2014"},{"key":"2023021801103382700_rssb12178-cit-0002","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/j.2517-6161.1993.tb01923.x","article-title":"On the use of nonparametric regression for checking linear relationships","volume":"55","author":"Azzalini","year":"1993","journal-title":"J. R. Statist. Soc."},{"key":"2023021801103382700_rssb12178-cit-0003","volume-title":"Convex Analysis and Optimization","author":"Bertsekas","year":"2003"},{"key":"2023021801103382700_rssb12178-cit-0004","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1198\/jasa.2009.tm08697","article-title":"Alternative goodness-of-fit tests for linear models","volume":"105","author":"Christensen","year":"2010","journal-title":"J. Am. Statist. Ass."},{"key":"2023021801103382700_rssb12178-cit-0005","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1214\/aos\/1176350693","article-title":"Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models","volume":"16","author":"Cox","year":"1988","journal-title":"Ann. Statist."},{"key":"2023021801103382700_rssb12178-cit-0006","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1080\/01621459.1990.10476211","article-title":"Testing the goodness of fit of a linear model via nonparametric regression techniques","volume":"85","author":"Eubank","year":"1990","journal-title":"J. Am. Statist. Ass."},{"key":"2023021801103382700_rssb12178-cit-0007","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1198\/016214501753168316","article-title":"Goodness-of-fit tests for parametric regression models","volume":"96","author":"Fan","year":"2001","journal-title":"J. Am. Statist. Ass."},{"key":"2023021801103382700_rssb12178-cit-0008","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1198\/016214504000001439","article-title":"Nonparametric inferences for additive models","volume":"100","author":"Fan","year":"2005","journal-title":"J. Am. Statist. Ass."},{"key":"2023021801103382700_rssb12178-cit-0009","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s11749-007-0080-8","article-title":"Nonparametric inference with generalized likelihood ratio tests","volume":"16","author":"Fan","year":"2007","journal-title":"Test"},{"key":"2023021801103382700_rssb12178-cit-0010","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1006\/jeem.1996.0052","article-title":"On the Harrison and Rubinfeld data","volume":"31","author":"Gilley","year":"1996","journal-title":"J. Environ. Econ. Mangmnt"},{"key":"2023021801103382700_rssb12178-cit-0011","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1214\/009053604000001200","article-title":"Data-driven rate-optimal specification testing in regression models","volume":"33","author":"Guerre","year":"2005","journal-title":"Ann. Statist."},{"key":"2023021801103382700_rssb12178-cit-0012","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s00440-014-0595-3","article-title":"Global risk bounds and adaptation in univariate convex regression","volume":"163","author":"Guntuboyina","year":"2015","journal-title":"Probab. Theor. Reltd Flds"},{"key":"2023021801103382700_rssb12178-cit-0013","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1214\/aos\/1176349403","article-title":"Comparing nonparametric versus parametric regression fits","volume":"21","author":"H\u00e4rdle","year":"1993","journal-title":"Ann. Statist."},{"key":"2023021801103382700_rssb12178-cit-0014","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0095-0696(78)90006-2","article-title":"Hedonic housing prices and the demand for clean air","volume":"5","author":"Harrison","year":"1978","journal-title":"J. Environ. Econ. Mangmnt"},{"key":"2023021801103382700_rssb12178-cit-0015","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1111\/j.1368-423X.2008.00239.x","article-title":"Representation theorem for convex nonparametric least squares","volume":"11","author":"Kuosmanen","year":"2008","journal-title":"Econmetr. J."},{"key":"2023021801103382700_rssb12178-cit-0016","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1287\/ijoc.2013.0587","article-title":"On convergence rates of convex regression in multiple dimensions","volume":"26","author":"Lim","year":"2014","journal-title":"INFORMS J. Comput."},{"key":"2023021801103382700_rssb12178-cit-0017","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1287\/opre.1110.1007","article-title":"Consistency of multidimensional convex regression","volume":"60","author":"Lim","year":"2012","journal-title":"Oper. Res."},{"key":"2023021801103382700_rssb12178-cit-0501","volume-title":"A computational framework for multivariate convex regression and its variants","author":"Mazumder","year":"2015"},{"key":"2023021801103382700_rssb12178-cit-0018","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0378-3758(99)00025-7","article-title":"An extension of the mixed primal-dual bases algorithm to the case of more constraints than dimensions","volume":"81","author":"Meyer","year":"1999","journal-title":"J. Statist. Planng Inf."},{"key":"2023021801103382700_rssb12178-cit-0019","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1080\/03610918.2012.659820","article-title":"A simple new algorithm for quadratic programming with applications in statistics","volume":"42","author":"Meyer","year":"2013","journal-title":"Communs Statist. Simuln Computn"},{"key":"2023021801103382700_rssb12178-cit-0020","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1080\/10485252.2013.797577","article-title":"Semi-parametric additive constrained regression","volume":"25","author":"Meyer","year":"2013","journal-title":"J. Nonparam. Statist."},{"key":"2023021801103382700_rssb12178-cit-0021","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1016\/j.jmva.2010.01.007","article-title":"Estimating the error distribution in nonparametric multiple regression with applications to model testing","volume":"101","author":"Neumeyer","year":"2010","journal-title":"J. Multiv. Anal."},{"key":"2023021801103382700_rssb12178-cit-0022","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1093\/oxfordjournals.aje.a115365","article-title":"Determinants of plasma levels of beta-carotene and retinol","volume":"130","author":"Nierenberg","year":"1989","journal-title":"Am. J. Epidem."},{"key":"2023021801103382700_rssb12178-cit-0023","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1198\/016214505000000637","article-title":"Global validation of linear model assumptions","volume":"101","author":"Pe\u00f1a","year":"2006","journal-title":"J. Am. Statist. Ass."},{"key":"2023021801103382700_rssb12178-cit-0024","doi-asserted-by":"crossref","first-page":"2809","DOI":"10.1080\/03610928608829280","article-title":"Hypothesis tests for normals means constrained by linear inequalities","volume":"15","author":"Raubertas","year":"1986","journal-title":"Communs Statist. Theor. Meth."},{"key":"2023021801103382700_rssb12178-cit-0025","volume-title":"Order Restricted Statistical Inference","author":"Robertson","year":"1988"},{"key":"2023021801103382700_rssb12178-cit-0026","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1214\/10-AOS852","article-title":"Nonparametric least squares estimation of a multivariate convex regression function","volume":"39","author":"Seijo","year":"2011","journal-title":"Ann. Statist."},{"key":"2023021801103382700_rssb12178-cit-0027","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1093\/biomet\/asu026","article-title":"Testing independence and goodness-of-fit in linear models","volume":"101","author":"Sen","year":"2014","journal-title":"Biometrika"},{"key":"2023021801103382700_rssb12178-cit-0028","volume-title":"Constrained Statistical Inference","author":"Silvapulle","year":"2005"},{"key":"2023021801103382700_rssb12178-cit-0029","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1214\/aos\/1031833666","article-title":"Nonparametric model checks for regression","volume":"25","author":"Stute","year":"1997","journal-title":"Ann. Statist."},{"key":"2023021801103382700_rssb12178-cit-0030","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/01621459.1998.10474096","article-title":"Bootstrap approximations in model checks for regression","volume":"93","author":"Stute","year":"1998","journal-title":"J. Am. Statist. Ass."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12178","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12178","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12178","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12178","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1111\/rssb.12178","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/79\/2\/423\/49232219\/jrsssb_79_2_423.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/79\/2\/423\/49232219\/jrsssb_79_2_423.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T23:11:09Z","timestamp":1718493069000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/79\/2\/423\/7041938"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,24]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,4,24]]},"published-print":{"date-parts":[[2017,3,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12178","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2017,3]]},"published":{"date-parts":[[2016,4,24]]}}}