{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T16:22:40Z","timestamp":1790785360140,"version":"4.1.0"},"reference-count":47,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T00:00:00Z","timestamp":1684108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of h \u2018good\u2019 observations among n observations and applies least squares on that subsample. We formulate a model in which this estimator is maximum likelihood. The model has \u2018outliers\u2019 of a new type, where the outlying observations are drawn from a distribution with values outside the realized range of h \u2018good\u2019, normal observations. The LTS estimator is found to be h1\/2 consistent and asymptotically standard normal in the location-scale case. Consistent estimation of h is discussed. The model differs from the commonly used \u03f5-contamination models and opens the door for statistical discussion on contamination schemes, new methodological developments on tests for contamination as well as inferences based on the estimated good data.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad028","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T11:01:47Z","timestamp":1684148507000},"page":"886-912","source":"Crossref","is-referenced-by-count":13,"title":["A model where the least trimmed squares estimator is maximum likelihood"],"prefix":"10.1093","volume":"85","author":[{"given":"Vanessa","family":"Berenguer-Rico","sequence":"first","affiliation":[{"name":"Department of Economics, University of Oxford , Oxford , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S\u00f8ren","family":"Johansen","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Copenhagen , Copenhagen , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bent","family":"Nielsen","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Oxford , Oxford , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,5,15]]},"reference":[{"issue":"1","key":"2023071211303091700_qkad028-B1","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1214\/12-AOAS575","article-title":"Sparse least trimmed squares regression for analyzing high-dimensional large data sets","volume":"7","author":"Alfons","year":"2013","journal-title":"The Annals of Applied Statistics"},{"issue":"2","key":"2023071211303091700_qkad028-B2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jkss.2010.02.007","article-title":"The forward search: Theory and data analysis (with discussion)","volume":"39","author":"Atkinson","year":"2010","journal-title":"Journal of the Korean Statistical Society"},{"key":"2023071211303091700_qkad028-B3","volume-title":"Marked and weighted empirical processes of residuals with applications to robust regressions","author":"Berenguer-Rico","year":"2017"},{"key":"2023071211303091700_qkad028-B4","volume-title":"Convergence of probability measures","author":"Billingsley","year":"1968"},{"issue":"1","key":"2023071211303091700_qkad028-B5","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1214\/aos\/1176345702","article-title":"Nonparametric interval and point prediction using data trimmed by a Grubbs-type outlier rule","volume":"10","author":"Butler","year":"1982","journal-title":"The Annals of Statistics"},{"issue":"3","key":"2023071211303091700_qkad028-B6","doi-asserted-by":"crossref","first-page":"1385","DOI":"10.1214\/aos\/1176349264","article-title":"Asymptotics for the minimum covariance determinant estimator","volume":"21","author":"Butler","year":"1993","journal-title":"The Annals of Statistics"},{"issue":"1","key":"2023071211303091700_qkad028-B7","doi-asserted-by":"crossref","DOI":"10.2202\/1941-1928.1097","article-title":"Evaluating automatic model selection","volume":"3","author":"Castle","year":"2011","journal-title":"Journal of Time Series Econometrics"},{"key":"2023071211303091700_qkad028-B8","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ecosta.2021.05.004","article-title":"Robust discovery of regression models","volume":"26","author":"Castle","year":"2023","journal-title":"Econometrics and Statistics"},{"issue":"11","key":"2023071211303091700_qkad028-B9","doi-asserted-by":"crossref","first-page":"3967","DOI":"10.1016\/j.jspi.2005.05.004","article-title":"Least trimmed squares in nonlinear regression under dependence","volume":"136","author":"\u010c\u00ed\u017eek","year":"2005","journal-title":"Journal of Statistical Planning and Inference"},{"issue":"7","key":"2023071211303091700_qkad028-B10","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1080\/03610929208830889","article-title":"A class of high-breakdown scale estimators based on subranges","volume":"21","author":"Croux","year":"1992","journal-title":"Communications in Statistics - 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