Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood
Publikation: Working paper › Forskning
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Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood. / Berenguer-Rico, Vanessa; Johansen, Søren; Nielsen, Bent.
2019.Publikation: Working paper › Forskning
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TY - UNPB
T1 - Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood
AU - Berenguer-Rico, Vanessa
AU - Johansen, Søren
AU - Nielsen, Bent
PY - 2019/9/27
Y1 - 2019/9/27
N2 - 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.
AB - 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.
KW - Chebychev estimator
KW - LMS
KW - Uniform distribution
KW - Least squares estimator
KW - LTS
KW - Normal distribution
KW - Regression
KW - Robust statistics
KW - Chebychev estimator
KW - LMS
KW - Uniform distribution
KW - Least squares estimator
KW - LTS
KW - Normal distribution
KW - Regression
KW - Robust statistics
KW - C01
KW - C13
U2 - 10.2139/ssrn.3455870
DO - 10.2139/ssrn.3455870
M3 - Working paper
T3 - University of Copenhagen. Institute of Economics. Discussion Papers (Online)
BT - Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood
ER -
ID: 248551490