Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood

Publikation: Working paperForskning

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 <i>h</i>, a sub-sample of <i>h</i> 'good' observations among <i>n</i> 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 <i>h</i><sup>1/2</sup> consistent and asymptotically standard normal. The LMS estimator is found to be <i>h</i> consistent and asymptotically Laplace.
OriginalsprogEngelsk
Antal sider39
DOI
StatusUdgivet - 27 sep. 2019
NavnUniversity of Copenhagen. Institute of Economics. Discussion Papers (Online)
Nummer19-11
ISSN1601-2461

    Forskningsområder

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

ID: 248551490