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: University of Oxford, Postal: Department of Economics, University of Oxford, Oxford, OX1 3UQ, UK, and Mansfield College, Oxford, OX1 3TF
Bent Nielsen: University of Oxford, Postal: Department of Economics, University of Oxford, Oxford, OX1 3UQ, UK, and Nuffield College, Oxford, OX1 1NF, UK

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Chebychev estimator; LMS; Uniform distribution; Least squares estimator; LTS; Normal distribution; Regression; Robust statistics (search for similar items in EconPapers)
JEL-codes: C01 C13 (search for similar items in EconPapers)
Pages: 41
Date: 2019-09-19
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
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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