{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T07:16:58Z","timestamp":1774768618893,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2000,10,5]],"date-time":"2000-10-05T00:00:00Z","timestamp":970704000000},"content-version":"unspecified","delay-in-days":4,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2000,10]]},"abstract":"<jats:p>Consider the model <jats:italic>y<\/jats:italic> = <jats:bold>x<\/jats:bold>\u2032<jats:bold>\u03b2<\/jats:bold><jats:sub>0<\/jats:sub> \n+ f<jats:sup>*<\/jats:sup>(<jats:bold>z<\/jats:bold>) + \u03b5, where \u03b5 [d over =] \nN(0, \u03c3<jats:sub>0<\/jats:sub><jats:sup>2<\/jats:sup>). We calculate the smallest \nasymptotic variance that <jats:italic>n<\/jats:italic><jats:sup>1\/2<\/jats:sup> consistent regular \n(<jats:italic>n<\/jats:italic><jats:sup>1\/2<\/jats:sup>CR) estimators of <jats:bold>\u03b2<\/jats:bold><jats:sub>0<\/jats:sub> can \nhave when the only information we possess about <jats:italic>f<\/jats:italic><jats:sup>*<\/jats:sup> \nis that it has a certain shape. We focus on three particular cases: \n(i) when <jats:italic>f<\/jats:italic><jats:sup>*<\/jats:sup> is homogeneous of degree <jats:italic>r<\/jats:italic>, \n(ii) when <jats:italic>f<\/jats:italic><jats:sup>*<\/jats:sup> is concave, \n(iii) when <jats:italic>f<\/jats:italic><jats:sup>*<\/jats:sup> is decreasing. \nOur results show that in the class of all <jats:italic>n<\/jats:italic><jats:sup>1\/2<\/jats:sup>CR \nestimators of <jats:bold>\u03b2<\/jats:bold><jats:sub>0<\/jats:sub>, homogeneity of \n<jats:italic>f<\/jats:italic><jats:sup>*<\/jats:sup> may lead to substantial asymptotic efficiency gains \nin estimating <jats:bold>\u03b2<\/jats:bold><jats:sub>0<\/jats:sub>. In contrast, at least \nasymptotically, concavity and monotonicity of <jats:italic>f<\/jats:italic><jats:sup>*<\/jats:sup> do \nnot help in estimating <jats:bold>\u03b2<\/jats:bold><jats:sub>0<\/jats:sub> more efficiently, at \nleast for <jats:italic>n<\/jats:italic><jats:sup>1\/2<\/jats:sup>CR estimators of \n<jats:bold>\u03b2<\/jats:bold><jats:sub>0<\/jats:sub>.<\/jats:p>","DOI":"10.1017\/s0266466600165053","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:47:49Z","timestamp":1027777669000},"page":"729-739","source":"Crossref","is-referenced-by-count":13,"title":["LOCAL SEMIPARAMETRIC EFFICIENCY BOUNDS UNDER SHAPE RESTRICTIONS"],"prefix":"10.1017","volume":"16","author":[{"given":"Gautam","family":"Tripathi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2000,10,5]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600165053","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T20:13:32Z","timestamp":1557346412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600165053\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,10]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2000,10]]}},"alternative-id":["S0266466600165053"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600165053","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,10]]}}}