{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:28:59Z","timestamp":1750465739022},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2002,7,17]],"date-time":"2002-07-17T00:00:00Z","timestamp":1026864000000},"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":[[2002,10]]},"abstract":"<jats:p>We establish [square root]<jats:italic>n<\/jats:italic>-consistency and asymptotic normality \nof Han's (1987a, <jats:italic>Journal of Econometrics<\/jats:italic> 35, 191\u2013209) \nestimator of the parameters characterizing the transformation \nfunction in a semiparametric transformation model. We verify \na Vapnik\u2013Cervonenkis (VC) condition for the parameterizations \nof Box and Cox (1964, <jats:italic>Journal of the Royal Statistical Society, \nSeries B<\/jats:italic> 34, 187\u2013200) and Bickel and Doksum (1981, \n<jats:italic>Journal of the American Statistical Association<\/jats:italic> 76, \n296\u2013311). The verification establishes the VC property \nfor a class of sets generated by a nonlinear function of the \ntransformation parameters. We also introduce a new class of \nrank estimators for these parameters. These estimators require \nonly <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup> log<jats:italic>n<\/jats:italic>) computations \nto evaluate the criterion function, compared to \n<jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>4<\/jats:sup>) computations \nfor Han's estimator. We prove that these estimators are \nalso [square root]<jats:italic>n<\/jats:italic>-consistent and asymptotically normal. \nA simulation study compares two of the new estimators to Han's \nestimator, the fully parametric estimator of Bickel and Doksum (1981), \nand the nonlinear two-stage least squares estimator of Amemiya \nand Powell (1981, <jats:italic>Journal of Econometrics<\/jats:italic> 17, 351\u2013381).<\/jats:p>","DOI":"10.1017\/s0266466602185045","type":"journal-article","created":{"date-parts":[[2002,11,14]],"date-time":"2002-11-14T22:03:05Z","timestamp":1037311385000},"page":"1099-1120","source":"Crossref","is-referenced-by-count":7,"title":["RANK ESTIMATORS FOR A TRANSFORMATION MODEL"],"prefix":"10.1017","volume":"18","author":[{"given":"Elena","family":"Asparouhova","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Golanski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krzysztof","family":"Kasprzyk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert P.","family":"Sherman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tihomir","family":"Asparouhov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2002,7,17]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466602185045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:32:51Z","timestamp":1557189171000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466602185045\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,7,17]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["S0266466602185045"],"URL":"https:\/\/doi.org\/10.1017\/s0266466602185045","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,7,17]]}}}