{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:59:39Z","timestamp":1772794779991,"version":"3.50.1"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,2,1]],"date-time":"2009-02-01T00:00:00Z","timestamp":1233446400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2009,2]]},"abstract":"<jats:p>We consider the problem of estimating a nonparametric regression model containing categorical regressors only. We investigate the theoretical properties of least squares cross-validated smoothing parameter selection, establish the rate of convergence (to zero) of the smoothing parameters for relevant regressors, and show that there is a high probability that the smoothing parameters for irrelevant regressors converge to their upper bound values, thereby automatically smoothing out the irrelevant regressors. A small-scale simulation study shows that the proposed cross-validation-based estimator performs well in finite-sample settings.<\/jats:p>","DOI":"10.1017\/s0266466608090014","type":"journal-article","created":{"date-parts":[[2009,1,9]],"date-time":"2009-01-09T14:13:57Z","timestamp":1231510437000},"page":"1-42","source":"Crossref","is-referenced-by-count":24,"title":["NONPARAMETRIC ESTIMATION OF REGRESSION FUNCTIONS WITH DISCRETE REGRESSORS"],"prefix":"10.1017","volume":"25","author":[{"given":"Desheng","family":"Ouyang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeffrey S.","family":"Racine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,1]]},"reference":[{"key":"S0266466608090014_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2998560"},{"key":"S0266466608090014_ref5","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1993.1019"},{"key":"S0266466608090014_ref19","first-page":"485","article-title":"Cross-validated local linear nonparametric regression","volume":"14","author":"Li","year":"2004","journal-title":"Statistica Sinica"},{"key":"S0266466608090014_ref16","doi-asserted-by":"publisher","DOI":"10.1162\/003465303772815925"},{"key":"S0266466608090014_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349748"},{"key":"S0266466608090014_ref13","first-page":"227","article-title":"Regression smoothing parameters that are not far from their optimum","volume":"87","author":"H\u00e4rdle","year":"1992","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466608090014_ref1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/63.3.413"},{"key":"S0266466608090014_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/71.2.341"},{"key":"S0266466608090014_ref12","first-page":"86","article-title":"How far are automatically chosen regression smoothing parameters from their optimum?","volume":"83","author":"H\u00e4rdle","year":"1988","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466608090014_ref10","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000000548"},{"key":"S0266466608090014_ref15","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00442"},{"key":"S0266466608090014_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0010-4"},{"key":"S0266466608090014_ref30","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/68.1.301"},{"key":"S0266466608090014_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00157-X"},{"key":"S0266466608090014_ref8","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/68.1.287"},{"key":"S0266466608090014_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/3087429"},{"key":"S0266466608090014_ref11","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/75.3.541"},{"key":"S0266466608090014_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771562"},{"key":"S0266466608090014_ref27","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316849"},{"key":"S0266466608090014_ref29","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1980.10486142"},{"key":"S0266466608090014_ref2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1983.10478031"},{"key":"S0266466608090014_ref6","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00123"},{"key":"S0266466608090014_ref23","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1996.tb00294.x"},{"key":"S0266466608090014_ref18","volume-title":"U-Statistics: Theory and Practice","author":"Lee","year":"1990"},{"key":"S0266466608090014_ref17","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhh006"},{"key":"S0266466608090014_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4026-6"},{"key":"S0266466608090014_ref24","doi-asserted-by":"publisher","DOI":"10.1080\/07474930600972590"},{"key":"S0266466608090014_ref20","article-title":"Nonparametric estimation of conditional CDF and quantile functions with mixed categorical and continuous data","author":"Li","year":"2007","journal-title":"Journal of Business and Economic Statistics, forthcoming"},{"key":"S0266466608090014_ref9","doi-asserted-by":"publisher","DOI":"10.1162\/rest.89.4.784"},{"key":"S0266466608090014_ref22","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618757"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T20:20:26Z","timestamp":1554322826000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090014\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,2]]}},"alternative-id":["S0266466608090014"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090014","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2]]}}}