{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T15:00:31Z","timestamp":1777561231165,"version":"3.51.4"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"03","license":[{"start":{"date-parts":[[2018,9,4]],"date-time":"2018-09-04T00:00:00Z","timestamp":1536019200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p>We show boundedness in probability uniformly in sample size of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semicontinuous and sufficiently large for large argument. Particular cases are the Huber-skip and quantile regression. Boundedness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic regressors, including stationary and random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.<\/jats:p>","DOI":"10.1017\/s0266466618000257","type":"journal-article","created":{"date-parts":[[2018,9,4]],"date-time":"2018-09-04T08:42:34Z","timestamp":1536050554000},"page":"653-683","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["BOUNDEDNESS OF M-ESTIMATORS FOR LINEAR REGRESSION IN TIME SERIES"],"prefix":"10.1017","volume":"35","author":[{"given":"S\u00f8ren","family":"Johansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bent","family":"Nielsen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2018,9,4]]},"reference":[{"key":"S0266466618000257_ref13","volume-title":"Methodological Tools in Robust and Nonparametric Statistics","year":"2012"},{"key":"S0266466618000257_ref8","doi-asserted-by":"publisher","DOI":"10.3150\/11-BEJ368"},{"key":"S0266466618000257_ref12","doi-asserted-by":"publisher","DOI":"10.3150\/14-BEJ689"},{"key":"S0266466618000257_ref6","first-page":"3967","volume":"136","year":"2005","journal-title":"Journal of Statistical Planning and Inference"},{"key":"S0266466618000257_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697731"},{"key":"S0266466618000257_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177700166"},{"key":"S0266466618000257_ref10","volume-title":"Robust Statistics","year":"2009"},{"key":"S0266466618000257_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(88)90120-0"},{"key":"S0266466618000257_ref3","volume-title":"Convergence of Probability Measures","year":"1968"},{"key":"S0266466618000257_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP506"},{"key":"S0266466618000257_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1765(99)00254-2"},{"key":"S0266466618000257_ref22","first-page":"1","volume":"42","year":"2006","journal-title":"Kybernetika"},{"key":"S0266466618000257_ref21","volume-title":"Robust Statistics: Theory and Methods","year":"2006"},{"key":"S0266466618000257_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009191"},{"key":"S0266466618000257_ref19","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1994.1036"},{"key":"S0266466618000257_ref18","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345697"},{"key":"S0266466618000257_ref17","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000001114"},{"key":"S0266466618000257_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/1913643"},{"key":"S0266466618000257_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004400"},{"key":"S0266466618000257_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177703732"},{"key":"S0266466618000257_ref14","doi-asserted-by":"publisher","DOI":"10.2307\/3315522"},{"key":"S0266466618000257_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347871"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466618000257","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T12:55:36Z","timestamp":1556715336000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466618000257\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,4]]},"references-count":22,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["S0266466618000257"],"URL":"https:\/\/doi.org\/10.1017\/s0266466618000257","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,4]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2018\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}