{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T07:17:04Z","timestamp":1774768624868,"version":"3.50.1"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,6,1]],"date-time":"2009-06-01T00:00:00Z","timestamp":1243814400000},"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":[[2009,6]]},"abstract":"<jats:p>Consider the unconditional moment restriction E[<jats:bold>m<\/jats:bold>(<jats:bold>y<\/jats:bold>, <jats:italic>\u03c5<\/jats:italic>, <jats:bold>w<\/jats:bold>; <jats:bold>\u03c0<\/jats:bold><jats:sub>0<\/jats:sub>)\/<jats:italic>f<\/jats:italic><jats:sub><jats:italic>V<\/jats:italic>|<jats:bold>w<\/jats:bold><\/jats:sub> (<jats:italic>\u03c5<\/jats:italic>|<jats:bold>w<\/jats:bold>) \u2212<jats:bold>s<\/jats:bold> (<jats:bold>w<\/jats:bold>; <jats:bold>\u03c0<\/jats:bold><jats:sub>0<\/jats:sub>)] = 0, where <jats:bold>m<\/jats:bold>(\u00b7) and <jats:bold>s<\/jats:bold>(\u00b7) are known vector-valued functions of data (<jats:bold>y<\/jats:bold><jats:sup>\u252c<\/jats:sup>, <jats:italic>\u03c5<\/jats:italic>, <jats:bold>w<\/jats:bold><jats:sup>\u252c<\/jats:sup>)<jats:sup>\u252c<\/jats:sup>. The smallest asymptotic variance that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466609090732_eqi1\"><jats:alt-text>$\\root  \\of n $<\/jats:alt-text><\/jats:inline-graphic>-consistent regular estimators of <jats:bold><jats:italic>\u03c0<\/jats:italic><\/jats:bold><jats:sub>0<\/jats:sub> can have is calculated when <jats:italic>f<\/jats:italic><jats:sub><jats:italic>V<\/jats:italic>|<jats:bold>w<\/jats:bold><\/jats:sub>(\u00b7) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that \u201cplug-in\u201d kernel-based estimators of <jats:bold><jats:italic>\u03c0<\/jats:italic><\/jats:bold><jats:sub>0<\/jats:sub> constructed from this type of moment restriction, such as Lewbel (1998, <jats:italic>Econometrica<\/jats:italic> 66, 105\u2013121) and Lewbel (2007, <jats:italic>Journal of Econometrics<\/jats:italic> 141, 777\u2013806), are semiparametric efficient.<\/jats:p>","DOI":"10.1017\/s0266466609090732","type":"journal-article","created":{"date-parts":[[2009,5,26]],"date-time":"2009-05-26T09:32:22Z","timestamp":1243330342000},"page":"847-855","source":"Crossref","is-referenced-by-count":9,"title":["EFFICIENCY BOUNDS FOR SEMIPARAMETRIC ESTIMATION OF INVERSE CONDITIONAL-DENSITY-WEIGHTED FUNCTIONS"],"prefix":"10.1017","volume":"25","author":[{"given":"David T.","family":"Jacho-Ch\u00e1vez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,6,1]]},"reference":[{"key":"S0266466609090732_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(00)00090-7"},{"key":"S0266466609090732_ref11","doi-asserted-by":"publisher","DOI":"10.2307\/1913267"},{"key":"S0266466609090732_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.11.004"},{"key":"S0266466609090732_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(00)00015-4"},{"key":"S0266466609090732_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/2998542"},{"key":"S0266466609090732_ref10","doi-asserted-by":"publisher","DOI":"10.1002\/jae.3950050202"},{"key":"S0266466609090732_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(87)90015-7"},{"key":"S0266466609090732_ref1","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00470"},{"key":"S0266466609090732_ref4","doi-asserted-by":"publisher","DOI":"10.2307\/1912775"},{"key":"S0266466609090732_ref5","unstructured":"Jacho-Ch\u00e1vez D.T . (2006) Identification, estimation and efficiency of nonparametric and semiparametric models in microeconometrics. Ph.D. Dissertation, London School of Economics and Political Science."},{"key":"S0266466609090732_ref3","doi-asserted-by":"publisher","DOI":"10.2307\/2951584"},{"key":"S0266466609090732_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.06.005"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466609090732","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T14:56:43Z","timestamp":1554303403000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466609090732\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["S0266466609090732"],"URL":"https:\/\/doi.org\/10.1017\/s0266466609090732","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}