Models where the least trimmed squares and least median of squares estimators are maximum likelihood

Journal article

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.

Authors: Berenguer-Rico, V; Johansen, S; Nielsen, B

• Publication status: Not published
• Peer review status: Reviewed (other)
• Publication date: 2019-09-19
• Language: English
• Keywords: regression; LMS; Chebychev estimator; robust statistics; least squares estimator; C01; C13; LTS; uniform distribution; normal distribution