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, University of Oxford
Bent Nielsen: Department of Economics, University of Oxford

No 19-11, Discussion Papers from University of Copenhagen. 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 fi?nd, for a given h; a sub-sample of h '?good' ?observations among n observations and estimate the regression on that sub-sample. We fi?nd 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 h1/2 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)
JEL-codes: C01 C13 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2019-09-17
New Economics Papers: this item is included in nep-ore
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https://www.economics.ku.dk/research/publications/wp/dp_2019/1911.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:kud:kuiedp:1911

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