{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T16:57:02Z","timestamp":1792515422977,"version":"4.5.0"},"reference-count":22,"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":6465,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>The LAD estimator of the vector parameter in a linear regression is defined by minimizing the sum of the absolute values of the residuals. This paper provides a direct proof of asymptotic normality for the LAD estimator. The main theorem assumes deterministic carriers. The extension to random carriers includes the case of autoregressions whose error terms have finite second moments. For a first-order autoregression with Cauchy errors the LAD estimator is shown to converge at a 1\/<jats:italic>n<\/jats:italic> rate.<\/jats:p>","DOI":"10.1017\/s0266466600004394","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:45:16Z","timestamp":1236699916000},"page":"186-199","source":"Crossref","is-referenced-by-count":504,"title":["Asymptotics for Least Absolute Deviation Regression Estimators"],"prefix":"10.1017","volume":"7","author":[{"given":"David","family":"Pollard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600004394_ref010","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343843"},{"key":"S0266466600004394_ref007","volume-title":"Least Absolute Deviations: Theory, Applications, and Algorithms","author":"Bloomfield","year":"1983"},{"key":"S0266466600004394_ref008","unstructured":"8. Davis R.A. , Knight K. & Liu J. . M-estimation for autoregressions with infinite variance. Preprint (1990)."},{"key":"S0266466600004394_ref005","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1978.10480065"},{"key":"S0266466600004394_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(82)90070-7"},{"key":"S0266466600004394_ref002","volume-title":"Advanced Econometrics","author":"Amemiya","year":"1985"},{"key":"S0266466600004394_ref019","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"S0266466600004394_ref011","unstructured":"11. Knight K. A proof of asymptotic normality of LAD and L-estimates in linear regression. Preprint, University of Toronto (1989a)."},{"key":"S0266466600004394_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1912608"},{"key":"S0266466600004394_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/1913622"},{"key":"S0266466600004394_ref009","doi-asserted-by":"publisher","DOI":"10.1080\/02331888808802084"},{"key":"S0266466600004394_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345976"},{"key":"S0266466600004394_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/3315522"},{"key":"S0266466600004394_ref014","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993713"},{"key":"S0266466600004394_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5254-2"},{"key":"S0266466600004394_ref016","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011233"},{"key":"S0266466600004394_ref018","volume-title":"NSF-CBMS Regional Conference Series in Probability and Statistics","volume":"2.","author":"Pollard","year":"1990"},{"key":"S0266466600004394_ref017","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012394"},{"key":"S0266466600004394_ref020","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1980.10477560"},{"key":"S0266466600004394_ref021","unstructured":"21. Sanz G. n r-consistency of certain optimal estimators, 0 <r<\u00bd . Preprint, Universidad de Zaragoza, 1988."},{"key":"S0266466600004394_ref006","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1975.10479884"},{"key":"S0266466600004394_ref022","unstructured":"22. Van de Geer S. Asymptotic normality of minimum L 1-norm estimators in linear regression. Preprint, University of Bristol, 1988."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600004394","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T21:36:45Z","timestamp":1558129005000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600004394\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["S0266466600004394"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600004394","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}