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

Vanessa Berenguer-Rico, Søren Johansen, Bent Nielsen

Publikation: Working paper/Preprint Working paperForskning

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Abstract

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.
OriginalsprogEngelsk
UdgivelsesstedAarhus
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider41
StatusUdgivet - 19 sep. 2019
NavnCREATES Research Paper
Nummer2019/15

Emneord

  • Chebychev estimator
  • LMS
  • Uniform distribution
  • Least squares estimator
  • LTS
  • Normal distribution
  • Regression
  • Robust statistics

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