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, Oxford University
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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