Template-type: ReDIF-Paper 1.0
Author-Name: Vanessa Berenguer-Rico
Author-Workplace-Name: Department of Economics and Mansfield College, University of Oxford
Author-Email: vanessa.berenguer-rico@economics.ox.ac.uk
Author-Name: Søren Johansen
Author-Workplace-Name: University of Copenhagen and CREATES and Aarhus University
Author-Email: soren.johansen@econ.ku.dk
Author-Name: Bent Nielsen
Author-Workplace-Name: Department of Economics and Nuffield College, University of Oxford
Author-Email: bent.nielsen@economics.ox.ac.uk
Title: Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood
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 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 h^1=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.
Length: 39 pages
Creation-Date: 2019-09-01
Number: 2019-W05
File-URL: https://www.nuffield.ox.ac.uk/economics/Papers/2019/2019W05_LTS_MLE_1sep2019.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:1905