{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T13:31:44Z","timestamp":1789392704889,"version":"build-2803163510"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":6738,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:p>We consider the linear regression model with censored dependent variable, where the disturbance terms are restricted only to have zero conditional median (or other prespecified quantile) given the regressors and the censoring point. Thus, the functional form of the conditional distribution of the disturbances is unrestricted, permitting heteroskedasticity of unknown form. For this model, a lower bound for the asymptotic covariance matrix for regular estimators of the regression coefficients is derived. This lower bound corresponds to the covariance matrix of an optimally weighted censored least absolute deviations estimator, where the optimal weight is the conditional density at zero of the disturbance. We also show how an estimator that attains this lower bound can be constructed, via nonparametric estimation of the conditional density at zero of the disturbance. As a special case our results apply to the (uncensored) linear model under a conditional median restriction.<\/jats:p>","DOI":"10.1017\/s0266466600005284","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:47:33Z","timestamp":1236685653000},"page":"295-317","source":"Crossref","is-referenced-by-count":96,"title":["Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions"],"prefix":"10.1017","volume":"6","author":[{"given":"Whitney K.","family":"Newey","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James L.","family":"Powell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600005284_ref037","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343886"},{"key":"S0266466600005284_ref013","volume-title":"Studies in Econometrics, Time Series, and Multivariate Statistics","author":"Goldberger","year":"1983"},{"key":"S0266466600005284_ref002","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.2307\/1912776","article-title":"An investigation of the robustness of the Tobit estimator to non-normality","volume":"50","author":"Abrazamar","year":"1982","journal-title":"Econometrica"},{"key":"S0266466600005284_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0027-2"},{"key":"S0266466600005284_ref034","doi-asserted-by":"publisher","DOI":"10.2307\/1911033"},{"key":"S0266466600005284_ref033","unstructured":"33. Ritov Y. Estimation in a linear regression model with censored data. Technical Report #114, Department of Statistics, UC Berkeley, 1987."},{"key":"S0266466600005284_ref032","unstructured":"32. Ritov Y. Efficient and unbiased estimation in nonparametric linear regression with censored data, manuscript, Department of Statistics, UC Berkeley, 1984."},{"key":"S0266466600005284_ref030","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90016-3"},{"key":"S0266466600005284_ref028","volume-title":"Some Basic Theory for Statistical Inference","author":"Pitman","year":"1979"},{"key":"S0266466600005284_ref026","article-title":"Semiparametric efficiency bounds","author":"Newey","journal-title":"Journal of Applied Econometrics"},{"key":"S0266466600005284_ref023","unstructured":"23. Newey W.K. Efficient estimation of models with conditional moment restrictions, manuscript, Department of Economics, Princeton University, 1987."},{"key":"S0266466600005284_ref008","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345987"},{"key":"S0266466600005284_ref025","volume-title":"Nonparametric and Semiparametric Methods in Econometrics and Statistics","author":"Newey"},{"key":"S0266466600005284_ref035","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350055"},{"key":"S0266466600005284_ref015","volume-title":"Theory of Rank Tests","author":"Hajek","year":"1967"},{"key":"S0266466600005284_ref031","doi-asserted-by":"publisher","DOI":"10.2307\/1914308"},{"key":"S0266466600005284_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350359"},{"key":"S0266466600005284_ref003","volume-title":"Asymptotics for semiparametric models II: Stochastic equicontinuity","author":"Andrews","year":"1989"},{"key":"S0266466600005284_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF00533669"},{"key":"S0266466600005284_ref017","unstructured":"17. Horowitz J.L. Semiparametric m-estimation of censored regression models, manuscript, Department of Economics, University of Iowa, 1987."},{"key":"S0266466600005284_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90010-2"},{"key":"S0266466600005284_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/1913600"},{"key":"S0266466600005284_ref029","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(84)90004-6"},{"key":"S0266466600005284_ref027","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5769-1"},{"key":"S0266466600005284_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90012-6"},{"key":"S0266466600005284_ref006","unstructured":"6. Bickel P. , Klaassen Y. Ritov , & J. Wellner . Efficient and adaptive inference in semiparametric models. Monograph, forthcoming, 1990."},{"key":"S0266466600005284_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(87)90015-7"},{"key":"S0266466600005284_ref019","volume-title":"Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability","author":"Huber","year":"1967"},{"key":"S0266466600005284_ref021","doi-asserted-by":"publisher","DOI":"10.1137\/1121087"},{"key":"S0266466600005284_ref001","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0304-4076(81)90029-4","article-title":"Further evidence on the robustness of the Tobit estimator to heteroscedasticity","volume":"17","author":"Abrazamar","year":"1981","journal-title":"Journal of Econometrics"},{"key":"S0266466600005284_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346151"},{"key":"S0266466600005284_ref022","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345644"},{"key":"S0266466600005284_ref036","volume-title":"Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability","volume":"1","author":"Stein","year":"1956"},{"key":"S0266466600005284_ref024","unstructured":"24. 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Efficient estimation of semiparametric models via moment restrictions, manuscript, Department of Economics, Princeton University, 1988."},{"key":"S0266466600005284_ref005","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345863"},{"key":"S0266466600005284_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90038-2"},{"key":"S0266466600005284_ref007","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/66.3.429"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600005284","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T16:21:32Z","timestamp":1558196492000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600005284\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0266466600005284"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600005284","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}