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

Vanessa Berenguer-Rico (), Soren Johansen and Bent Nielsen ()
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Vanessa Berenguer-Rico: Department of Economics and Mansfield College, University of Oxford
Bent Nielsen: Department of Economics and Nuffield College, University of Oxford

No 2019-W05, Economics Papers from Economics Group, Nuffield College, University of Oxford

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 h^1=2 consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.

Keywords: Chebychev estimator; LMS; Uniform distribution; Least squares estimator; LTS; Normal distribution; Regression; Robust statistics. (search for similar items in EconPapers)
Pages: 39 pages
Date: 2019-09-01
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Citations: View citations in EconPapers (2)

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https://www.nuffield.ox.ac.uk/economics/Papers/2019/2019W05_LTS_MLE_1sep2019.pdf (application/pdf)

Related works:
Working Paper: Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood (2019)
Working Paper: Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood (2019)
Working Paper: Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:nuf:econwp:1905

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