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

Vanessa Berenguer Rico, Bent Nielsen and Soren Johansen

No 879, Economics Series Working Papers from University of Oxford, Department of Economics

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)
Date: 2019-09-04
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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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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