{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T20:26:35Z","timestamp":1790799995306,"version":"4.1.0"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5369,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1994,6]]},"abstract":"<jats:p>We prove <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466600008458_inline1\"\/>-consistency and asymptotic normality of a generalized semiparametric regression estimator that includes as special cases Ichimura's semiparametric least-squares estimator for single index models, and the estimator of Klein and Spady for the binary choice regression model. Two function expansions reveal a type of U-process structure in the criterion function; then new U-process maximal inequalities are applied to establish the requisite stochastic equicontinuity condition. This method of proof avoids much of the technical detail required by more traditional methods of analysis. The general framework suggests other <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466600008458_inline1\"\/>-consistent and asymptotically normal estimators.<\/jats:p>","DOI":"10.1017\/s0266466600008458","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:43:23Z","timestamp":1236685403000},"page":"372-395","source":"Crossref","is-referenced-by-count":50,"title":["U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator"],"prefix":"10.1017","volume":"10","author":[{"given":"Robert P.","family":"Sherman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600008458_ref019","doi-asserted-by":"publisher","DOI":"10.2307\/2951780"},{"key":"S0266466600008458_ref017","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316481"},{"key":"S0266466600008458_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/1913622"},{"key":"S0266466600008458_ref013","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350374"},{"key":"S0266466600008458_ref010","volume-title":"Semiparametric estimation of multiple indices models: single equation estimation","author":"Ichimura","year":"1988"},{"key":"S0266466600008458_ref009","volume-title":"Semiparametric least squares estimation of single index models","author":"Ichimura","year":"1988"},{"key":"S0266466600008458_ref008","first-page":"221","volume-title":"Fifth Berkeley Symposium on Mathematical Statistics and Probability","author":"Huber","year":"1967"},{"key":"S0266466600008458_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/1913600"},{"key":"S0266466600008458_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90038-2"},{"key":"S0266466600008458_ref003","volume-title":"Asymptotics for semiparametric econometric models III. testing and examples","author":"Andrews","year":"1989"},{"key":"S0266466600008458_ref001","volume-title":"Asymptotics for semiparametric econometric models I. estimation","author":"Andrews","year":"1989"},{"key":"S0266466600008458_ref004","volume-title":"Kernel estimators for regression functions","author":"Bierens","year":"1985"},{"key":"S0266466600008458_ref012","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346523"},{"key":"S0266466600008458_ref018","article-title":"Maximal inequalities for degenerate U-processes with applications to optimization estimators","author":"Sherman","journal-title":"Annals of Statistics"},{"key":"S0266466600008458_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/2951556"},{"key":"S0266466600008458_ref014","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011233"},{"key":"S0266466600008458_ref016","unstructured":"16. Pollard D. Unpublished lecture notes for an asymptotic methods course taught at Yale University, 1989."},{"key":"S0266466600008458_ref007","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177703732"},{"key":"S0266466600008458_ref002","volume-title":"Asymptotics for semiparametric econometric models II. stochastic equicontinuity","author":"Andrews","year":"1989"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600008458","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T23:53:24Z","timestamp":1557878004000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600008458\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,6]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,6]]}},"alternative-id":["S0266466600008458"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600008458","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,6]]}}}