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

Research output: Working paper › Research

- Vanessa Berenguer-Rico, University of Oxford, Oxford, United Kingdom
- Søren Johansen
- Bent Nielsen, Oxford University

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.

Original language | English |
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Place of publication | Aarhus |
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Publisher | Institut for Økonomi, Aarhus Universitet |
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Number of pages | 41 |
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Publication status | Published - 19 Sep 2019 |
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Series | CREATES Research Papers |
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Number | 2019/15 |
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Citationformats

ID: 165609506