Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood
Research output: Working paper
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 h1/2 consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.
Original language | English |
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Number of pages | 39 |
DOIs | |
Publication status | Published - 27 Sep 2019 |
Series | University of Copenhagen. Institute of Economics. Discussion Papers (Online) |
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Number | 19-11 |
ISSN | 1601-2461 |
- Chebychev estimator, LMS, Uniform distribution, Least squares estimator, LTS, Normal distribution, Regression, Robust statistics, C01, C13
Research areas
Links
- https://www.economics.ku.dk/research/publications/wp/dp_2019/1911.pdf
Submitted manuscript
ID: 248551490