{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T10:18:42Z","timestamp":1790417922458,"version":"4.1.0"},"reference-count":71,"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":5004,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1995,6]]},"abstract":"<jats:p>This paper develops the asymptotic theory for least absolute deviation estimation of a shift in linear regressions. Rates of convergence and asymptotic distributions for the estimated regression parameters and the estimated shift point are derived. The asymptotic theory is developed both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases. Asymptotic distributions are also obtained for trending regressors and for dependent disturbances. The analysis is carried out in the framework of partial structural change, allowing some parameters not to be influenced by the shift. Efficiency relative to least-squares estimation is also discussed. Monte Carlo analysis is performed to assess how informative the asymptotic distributions are.<\/jats:p>","DOI":"10.1017\/s026646660000935x","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:43:14Z","timestamp":1236685394000},"page":"403-436","source":"Crossref","is-referenced-by-count":88,"title":["Least Absolute Deviation Estimation of a Shift"],"prefix":"10.1017","volume":"11","author":[{"given":"Jushan","family":"Bai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S026646660000935X_ref026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-48412-4_9"},{"key":"S026646660000935X_ref048","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005284"},{"key":"S026646660000935X_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2938229"},{"key":"S026646660000935X_ref068","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/73.1.91"},{"key":"S026646660000935X_ref067","first-page":"180","article-title":"On the likelihood ratio test for a shift in locations of normal populations","volume":"72","author":"Worsley","year":"1979","journal-title":"Journal of the American Statistical Association"},{"key":"S026646660000935X_ref064","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004230"},{"key":"S026646660000935X_ref062","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1975.10489272"},{"key":"S026646660000935X_ref051","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/07350015.1992.10509907","article-title":"Nonstationarity and level shifts with an application to purchasing power parity","volume":"10","author":"Perron","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S026646660000935X_ref066","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012032"},{"key":"S026646660000935X_ref071","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1080\/07474939408800290","article-title":"A Bayesian analysis of trend determination in economics time series","volume":"13","author":"Zivot","year":"1994","journal-title":"Econometric Reviews"},{"key":"S026646660000935X_ref059","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1958.10501484"},{"key":"S026646660000935X_ref053","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004709"},{"key":"S026646660000935X_ref028","first-page":"1179","article-title":"The influence curve and its role in robust estimation","volume":"62","author":"Hampel","year":"1974","journal-title":"Journal of the American Statistical Association"},{"key":"S026646660000935X_ref052","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(85)90031-6"},{"key":"S026646660000935X_ref038","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.1.71"},{"key":"S026646660000935X_ref021","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1080\/07350015.1992.10509906","article-title":"A direct test for changing trend","volume":"10","author":"Chu","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S026646660000935X_ref017","doi-asserted-by":"publisher","DOI":"10.2307\/2951618"},{"key":"S026646660000935X_ref016","volume-title":"Econometrics and Structural Change","author":"Broemeling","year":"1987"},{"key":"S026646660000935X_ref012","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S026646660000935X_ref058","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(84)90004-6"},{"key":"S026646660000935X_ref046","first-page":"375","volume-title":"Handbook of Statistics","volume":"7","author":"Krishnaiah","year":"1988"},{"key":"S026646660000935X_ref056","doi-asserted-by":"crossref","unstructured":"Pollard D. (1990) Empirical Processes: Theory and Applications, vol. 2. CBMS Conference Series in Probability and Statistics. Hayward, CA: Institute of Mathematical Statistics.","DOI":"10.1214\/cbms\/1462061091"},{"key":"S026646660000935X_ref045","doi-asserted-by":"publisher","DOI":"10.2307\/1913102"},{"key":"S026646660000935X_ref070","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-589320-6.50016-2"},{"key":"S026646660000935X_ref004","volume-title":"Optimal Tests of Parameter Constancy","author":"Andrews","year":"1992"},{"key":"S026646660000935X_ref020","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1080\/07350015.1992.10509903","article-title":"Searching for a break in GNP","volume":"10","author":"Christiano","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S026646660000935X_ref069","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350509"},{"key":"S026646660000935X_ref047","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(88)90045-2"},{"key":"S026646660000935X_ref014","volume-title":"Least Absolute Deviations, Theory, Applications, and Algorithms","author":"Bloomfield","year":"1983"},{"key":"S026646660000935X_ref024","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343241"},{"key":"S026646660000935X_ref057","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004394"},{"key":"S026646660000935X_ref055","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5254-2"},{"key":"S026646660000935X_ref049","doi-asserted-by":"publisher","DOI":"10.2307\/1913610"},{"key":"S026646660000935X_ref030","first-page":"655","article-title":"A simple least square method for estimating a change in mean","volume":"15","author":"Hawkins","year":"1986","journal-title":"Communications in Statistics\u2013Simulations"},{"key":"S026646660000935X_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1912608"},{"key":"S026646660000935X_ref025","volume-title":"Nonparametric Curve Estimation from Time Series","author":"Gyorfi","year":"1990"},{"key":"S026646660000935X_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(87)90152-7"},{"key":"S026646660000935X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01845702"},{"key":"S026646660000935X_ref034","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1982.10477763"},{"key":"S026646660000935X_ref044","doi-asserted-by":"publisher","DOI":"10.2307\/1912528"},{"key":"S026646660000935X_ref063","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177696898"},{"key":"S026646660000935X_ref019","volume-title":"Quantile Regression, Censoring, and Structure of Wage","author":"Chamberlain","year":"1991"},{"key":"S026646660000935X_ref050","volume-title":"Trend, Unit Root and Structural Change in Macroeconomic Time Series","author":"Perron","year":"1993"},{"key":"S026646660000935X_ref061","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOAS211"},{"key":"S026646660000935X_ref035","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(82)90052-5"},{"key":"S026646660000935X_ref037","volume-title":"Independent and Stationary Sequences of Random Variables","author":"Ibragimov","year":"1971"},{"key":"S026646660000935X_ref041","doi-asserted-by":"publisher","DOI":"10.2307\/3315522"},{"key":"S026646660000935X_ref013","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704964"},{"key":"S026646660000935X_ref042","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004400"},{"key":"S026646660000935X_ref043","doi-asserted-by":"publisher","DOI":"10.2307\/1913643"},{"key":"S026646660000935X_ref036","doi-asserted-by":"publisher","DOI":"10.1002\/0471725250"},{"key":"S026646660000935X_ref027","volume-title":"Bootstrapping Quantile Regression Models","author":"Hahn","year":"1992"},{"key":"S026646660000935X_ref010","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1978.10480065"},{"key":"S026646660000935X_ref065","doi-asserted-by":"publisher","DOI":"10.1007\/BF01025869"},{"key":"S026646660000935X_ref023","volume-title":"An Introduction to Probability Theory and Its Applications","author":"Feller","year":"1971"},{"key":"S026646660000935X_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-8162-8_8"},{"key":"S026646660000935X_ref008","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1994.tb00204.x"},{"key":"S026646660000935X_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350699"},{"key":"S026646660000935X_ref031","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1977.10479935"},{"key":"S026646660000935X_ref054","doi-asserted-by":"publisher","DOI":"10.2307\/1427090"},{"key":"S026646660000935X_ref029","first-page":"321","article-title":"Tests for parameter instability in regressions with I(1) processes","volume":"10","author":"Hansen","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S026646660000935X_ref039","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347498"},{"key":"S026646660000935X_ref022","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348257"},{"key":"S026646660000935X_ref060","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.42.1.43"},{"key":"S026646660000935X_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2951764"},{"key":"S026646660000935X_ref007","volume-title":"Estimation of Structural Change Based on Wald Type Statistics","author":"Bai","year":"1994"},{"key":"S026646660000935X_ref006","volume-title":"LAD Estimation of a Shift","author":"Bai","year":"1993"},{"key":"S026646660000935X_ref033","doi-asserted-by":"publisher","DOI":"10.2307\/2951583"},{"key":"S026646660000935X_ref032","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/57.1.1"},{"key":"S026646660000935X_ref040","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/76.3.409"},{"key":"S026646660000935X_ref009","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1080\/07350015.1992.10509905","article-title":"Recursive and sequential tests of the unit root and trend break hypothesis, theory and international evidence","volume":"10","author":"Banerjee","year":"1992","journal-title":"Journal of Business and Economic Statistics"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026646660000935X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T00:46:33Z","timestamp":1738975593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026646660000935X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":71,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S026646660000935X"],"URL":"https:\/\/doi.org\/10.1017\/s026646660000935x","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}