{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T11:43:13Z","timestamp":1791978193905,"version":"4.4.0"},"reference-count":24,"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":4638,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:p>We consider the following linear regression model:<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466600006587_eqnU1\"\/><\/jats:disp-formula><\/jats:p><jats:p>where<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466600006587_inline1\"\/>are independent and identically distributed random variables, Y<jats:sub>i<\/jats:sub>, is real, Z<jats:sub>i<\/jats:sub>has values in R<jats:sup>m<\/jats:sup>, U<jats:sub>i<\/jats:sub>, is independent of Z<jats:sub>i<\/jats:sub>, and \u03b8<jats:sub>0<\/jats:sub>is an<jats:italic>m<\/jats:italic>-dimensional parameter to be estimated. The<jats:italic>L<jats:sub>p<\/jats:sub><\/jats:italic>estimator of \u03b8<jats:sub>0<\/jats:sub>is the value 6n such that<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466600006587_eqnU2\"\/><\/jats:disp-formula><\/jats:p><jats:p>Here, we will give the exact Bahadur-Kiefer representation of \u03b8n, for each p \u2265 1. Explicitly, we will see that, under regularity conditions,<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466600006587_eqnU3\"\/><\/jats:disp-formula><\/jats:p><jats:p>where<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466600006587_inline2\"\/><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466600006587_inline3\"\/>and<jats:italic>c<\/jats:italic>is a positive constant, which depends on<jats:italic>p<\/jats:italic>and on the random variable<jats:italic>X<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0266466600006587","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:41:30Z","timestamp":1236699690000},"page":"257-283","source":"Crossref","is-referenced-by-count":21,"title":["The Bahadur-Kiefer Representation of<i>L<sub>p<\/sub><\/i>Regression Estimators"],"prefix":"10.1017","volume":"12","author":[{"given":"Miguel A.","family":"Arcones","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600006587_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5254-2"},{"key":"S0266466600006587_ref017","first-page":"851","article-title":"L-estimation for linear models","volume":"82","author":"Koenker","year":"1987","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600006587_ref016","first-page":"263","article-title":"Uniform second order asymptotic linearity of M-statistics in linear models","volume":"7","author":"Jure\u010dkov\u00e1","year":"1989","journal-title":"Statistics and Decisions"},{"key":"S0266466600006587_ref015","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343843"},{"key":"S0266466600006587_ref022","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1980.10477560"},{"key":"S0266466600006587_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991688"},{"key":"S0266466600006587_ref020","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004394"},{"key":"S0266466600006587_ref012","unstructured":"He X. & Shao Q.M. (1993) A Strong Bahadur-Kiefer Representation of Lp Regression Estimators. 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