Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood

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  • Vanessa Berenguer-Rico, University of Oxford, Oxford, United Kingdom
  • Søren Johansen
  • Bent Nielsen, University of Oxford
The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h, a sub-sample of h `good' observations among n observations and estimate the regression on that sub-sample. We find models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be sqrt(h) consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages41
Publication statusPublished - 19 Sep 2019
SeriesCREATES Research Papers
Number2019/15

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