{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T06:42:00Z","timestamp":1776753720346,"version":"3.51.2"},"reference-count":44,"publisher":"Elsevier BV","issue":"9","license":[{"start":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T00:00:00Z","timestamp":1346457600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational Statistics &amp; Data Analysis"],"published-print":{"date-parts":[[2012,9]]},"DOI":"10.1016\/j.csda.2012.02.018","type":"journal-article","created":{"date-parts":[[2012,3,6]],"date-time":"2012-03-06T08:46:53Z","timestamp":1331023613000},"page":"2729-2741","source":"Crossref","is-referenced-by-count":93,"title":["Shape restricted nonparametric regression with Bernstein polynomials"],"prefix":"10.1016","volume":"56","author":[{"given":"J.","family":"Wang","sequence":"first","affiliation":[]},{"given":"S.K.","family":"Ghosh","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.csda.2012.02.018_br000005","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/S0304-4076(03)00102-7","article-title":"Nonparametric option pricing under shape restrictions","volume":"116","author":"A\u00eft-Sahalia","year":"2003","journal-title":"Journal of Econometrics"},{"key":"10.1016\/j.csda.2012.02.018_br000010","series-title":"Statistical Inference Under Order Restrictions","author":"Barlow","year":"1972"},{"key":"10.1016\/j.csda.2012.02.018_br000015","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1111\/j.1467-9469.2006.00534.x","article-title":"Estimating a convex function in nonparametric regression","volume":"34","author":"Birke","year":"2007","journal-title":"Scandinavian Journal of Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000020","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1198\/tast.2009.08191","article-title":"A note on B-splines for semiparametric elicitation","volume":"63","author":"Bornkamp","year":"2009","journal-title":"The American Statistician"},{"issue":"4","key":"10.1016\/j.csda.2012.02.018_br000025","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1214\/aoms\/1177728420","article-title":"Maximum likelihood estimates of monotone parameters","volume":"26","author":"Brunk","year":"1955","journal-title":"The Annals of Mathematical Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000030","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF02071384","article-title":"Shape preserving representations and optimality of the Bernstein basis","volume":"1","author":"Carnicer","year":"1993","journal-title":"Advances in Computational Mathematics"},{"key":"10.1016\/j.csda.2012.02.018_br000035","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.econlet.2005.01.025","article-title":"Semi-nonparametric estimation with Bernstein polynomials","volume":"89","author":"Chak","year":"2005","journal-title":"Economics Letters"},{"key":"10.1016\/j.csda.2012.02.018_br000040","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1111\/j.1467-9469.2005.00451.x","article-title":"Bayesian survival analysis using Bernstein polynomials","volume":"32","author":"Chang","year":"2005","journal-title":"Scandinavian Journal of Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000045","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1214\/074921707000000157","article-title":"Shape restricted regression with random Bernstein polynomials","volume":"54","author":"Chang","year":"2007","journal-title":"Lecture Notes-Monograph Series"},{"key":"10.1016\/j.csda.2012.02.018_br000050","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1080\/02664761003692423","article-title":"A variable selection approach to monotonic regression with Bernstein polynomials","volume":"38","author":"Curtis","year":"2011","journal-title":"Journal of Applied Statistics"},{"issue":"3","key":"10.1016\/j.csda.2012.02.018_br000055","doi-asserted-by":"crossref","first-page":"469","DOI":"10.3150\/bj\/1151525131","article-title":"A simple nonparametric estimator of a strictly monotone regression function","volume":"12","author":"Dette","year":"2006","journal-title":"Bernoulli"},{"key":"10.1016\/j.csda.2012.02.018_br000060","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF02237820","article-title":"An algorithm for cubic spline fitting with convexity constraints","volume":"24","author":"Dierckx","year":"1980","journal-title":"Computing"},{"key":"10.1016\/j.csda.2012.02.018_br000065","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1007\/BF02237820","article-title":"An algorithm for restricted least squares regression","volume":"78","author":"Dykstra","year":"1983","journal-title":"Journal of the American Statistical Association"},{"key":"10.1016\/j.csda.2012.02.018_br000070","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2307\/2288193","article-title":"A mixed prinmal-dual bases algorithm for regression under inequality constraints: application to concave regression","volume":"16","author":"Fraser","year":"1989","journal-title":"Scandinavian Journal of Statistics"},{"issue":"3","key":"10.1016\/j.csda.2012.02.018_br000075","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/00401706.1984.10487961","article-title":"The monotone smoothing of scatterplots","volume":"26","author":"Friedman","year":"1984","journal-title":"Technometrics"},{"key":"10.1016\/j.csda.2012.02.018_br000080","doi-asserted-by":"crossref","first-page":"295","DOI":"10.2307\/1267550","article-title":"Imposing curvature restrictions on flexible functional forms","volume":"38","author":"Gallant","year":"1984","journal-title":"Journal of Econometrics"},{"key":"10.1016\/j.csda.2012.02.018_br000085","series-title":"Numerical Analysis","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/0304-4076(84)90024-1","article-title":"Dual and primal-dual methods for solving strictly convex quadratic programs","volume":"No. 909","author":"Goldfarb","year":"1982"},{"key":"10.1016\/j.csda.2012.02.018_br000090","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02591962","article-title":"A numerically stable dual method for solving strictly convex quadratic programs","volume":"27","author":"Goldfarb","year":"1983","journal-title":"Mathematical Programming"},{"key":"10.1016\/j.csda.2012.02.018_br000095","series-title":"Matrix Computations","doi-asserted-by":"crossref","DOI":"10.1007\/BF02591962","author":"Golub","year":"1996"},{"key":"10.1016\/j.csda.2012.02.018_br000100","series-title":"Abstract Inference (Probability & Mathematical Statistics)","author":"Grenander","year":"1981"},{"key":"10.1016\/j.csda.2012.02.018_br000105","first-page":"1653","article-title":"Estimation of convex functions: characterizations and asymptotic theory","volume":"26","author":"Groeneboom","year":"2001","journal-title":"The Annual of Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000110","series-title":"A Distribution-Free Theory of Nonparametric Regression","author":"Gyorfi","year":"2002"},{"issue":"3","key":"10.1016\/j.csda.2012.02.018_br000115","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1214\/aos\/1009210683","article-title":"Nonparametric kernel regression subject to monotonicity constraints","volume":"29","author":"Hall","year":"2001","journal-title":"Annals of Statistics"},{"issue":"1","key":"10.1016\/j.csda.2012.02.018_br000120","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01580719","article-title":"A successive projection method","volume":"40","author":"Han","year":"1988","journal-title":"Mathematical Programming"},{"key":"10.1016\/j.csda.2012.02.018_br000125","doi-asserted-by":"crossref","DOI":"10.1007\/BF01580719","author":"Hansen","year":"2010","journal-title":"Econometrics"},{"key":"10.1016\/j.csda.2012.02.018_br000130","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1214\/aos\/1176343640","article-title":"Consistency in concave regression","volume":"4","author":"Hanson","year":"1976","journal-title":"The Annals of Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000135","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1214\/aos\/1176343640","article-title":"The Bernstein polynomials for discontinuous functions","volume":"68","author":"Herzog","year":"1946","journal-title":"American Journal of Mathematics"},{"key":"10.1016\/j.csda.2012.02.018_br000140","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1080\/01621459.1954.10483523","article-title":"Point estimate of ordinates of concave functions","volume":"49","author":"Hildreth","year":"1954","journal-title":"Journal of the American Statistical Association"},{"key":"10.1016\/j.csda.2012.02.018_br000145","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.2307\/2532449","article-title":"Monotone smoothing with application to dose-response curves and the assessment of synergism","volume":"46","author":"Kelly","year":"1990","journal-title":"Biometrics"},{"key":"10.1016\/j.csda.2012.02.018_br000150","series-title":"Bernstein Polynomials","doi-asserted-by":"crossref","DOI":"10.2307\/2532449","author":"Lorentz","year":"1986"},{"key":"10.1016\/j.csda.2012.02.018_br000155","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1214\/aos\/1176348118","article-title":"Nonparametric regression under qualitative smoothness assumptions","volume":"19","author":"Mammen","year":"1991","journal-title":"The Annual of Statistics"},{"issue":"3","key":"10.1016\/j.csda.2012.02.018_br000160","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1214\/aos\/1176348118","article-title":"A general projection framework for constrained smoothing","volume":"16","author":"Mammen","year":"2001","journal-title":"Statistical Science"},{"issue":"3","key":"10.1016\/j.csda.2012.02.018_br000165","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1214\/ss\/1009213727","article-title":"Inference using shape-restricted regression splines","volume":"2","author":"Meyer","year":"2008","journal-title":"Annals of Applied Statistics"},{"issue":"2","key":"10.1016\/j.csda.2012.02.018_br000170","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1023\/A:1015122221315","article-title":"Bayesian analysis under ordered functions of parameters","volume":"9","author":"Molitor","year":"2002","journal-title":"Environmental and Ecological Statistics"},{"issue":"2","key":"10.1016\/j.csda.2012.02.018_br000175","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1214\/08-AOAS167","article-title":"Monotone nonparametric regression","volume":"16","author":"Mukerjee","year":"1988","journal-title":"The Annals of Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000180","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1023\/A:1015122221315","article-title":"Estimation of a polya frequency function","volume":"54","author":"Pal","year":"2007","journal-title":"IMS Lecture Notes Monograph Series"},{"key":"10.1016\/j.csda.2012.02.018_br000185","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1214\/aos\/1176350832","article-title":"Random Bernstein polynomials","volume":"26","author":"Petrone","year":"1999","journal-title":"Scandinavian Journal of Statistics"},{"issue":"4","key":"10.1016\/j.csda.2012.02.018_br000190","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1214\/074921707000000184","article-title":"Monotone regression splines in action","volume":"3","author":"Ramsay","year":"1988","journal-title":"Statistical Science"},{"issue":"2","key":"10.1016\/j.csda.2012.02.018_br000195","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1111\/1467-9469.00155","article-title":"Asymptotic properties of nonparametric curve estimates","volume":"17","author":"Stadtmuller","year":"1986","journal-title":"Periodica Methematrica Hungarica"},{"key":"10.1016\/j.csda.2012.02.018_br000200","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1214\/ss\/1177012761","article-title":"Incorporating monotonicity and concavity conditions in flexible function forms","volume":"11","author":"Terrell","year":"1996","journal-title":"Journal of Applied Econometrics"},{"key":"10.1016\/j.csda.2012.02.018_br000205","doi-asserted-by":"crossref","unstructured":"Turlach, B.A., Weingessel, A., 2010. Quadprog (Version 1.5-3), R package.","DOI":"10.1007\/BF01849318"},{"issue":"397","key":"10.1016\/j.csda.2012.02.018_br000210","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1002\/(SICI)1099-1255(199603)11:2<179::AID-JAE389>3.0.CO;2-G","article-title":"Inequality-constrained multivariate smoothing splines with application to the estimation of posterior probabilities","volume":"82","author":"Villalobos","year":"1987","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"10.1016\/j.csda.2012.02.018_br000215","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1198\/106186008X285627","article-title":"Isotonic smoothing spline regression","volume":"17","author":"Wang","year":"2008","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"10.1016\/j.csda.2012.02.018_br000220","first-page":"105","article-title":"Some algorithms for concave and isotonic regression","volume":"19","author":"Wu","year":"1982","journal-title":"Studies in the Management Sciences"}],"container-title":["Computational Statistics &amp; Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947312001004?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947312001004?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T15:50:44Z","timestamp":1641052244000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947312001004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":44,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0167947312001004"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2012.02.018","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}