Research output: Working paper › Research

**Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood.** / Berenguer-Rico, Vanessa; Johansen, Søren; Nielsen, Bent.

Research output: Working paper › Research

Berenguer-Rico, V, Johansen, S & Nielsen, B 2019 'Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood' Institut for Økonomi, Aarhus Universitet, Aarhus.

Berenguer-Rico, V., Johansen, S., & Nielsen, B. (2019). *Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood*. Aarhus: Institut for Økonomi, Aarhus Universitet. CREATES Research Papers, No. 2019/15

Berenguer-Rico V, Johansen S, Nielsen B. 2019. Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood. Aarhus: Institut for Økonomi, Aarhus Universitet.

Berenguer-Rico, Vanessa, Søren Johansen and Bent Nielsen *Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood*. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2019/15). 2019., 41 p.

Berenguer-Rico V, Johansen S, Nielsen B. Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood. Aarhus: Institut for Økonomi, Aarhus Universitet. 2019 Sep 19.

Berenguer-Rico, Vanessa ; Johansen, Søren ; Nielsen, Bent. / **Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood**. Aarhus : Institut for Økonomi, Aarhus Universitet, 2019. (CREATES Research Papers; No. 2019/15).

@techreport{64e5b522c2ac405a978a2fdc6241f384,

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 sqrt(h) 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",

author = "Vanessa Berenguer-Rico and S{\o}ren Johansen and Bent Nielsen",

year = "2019",

month = "9",

day = "19",

language = "English",

publisher = "Institut for {\O}konomi, Aarhus Universitet",

type = "WorkingPaper",

institution = "Institut for {\O}konomi, Aarhus Universitet",

}

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 - 2019/9/19

Y1 - 2019/9/19

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 sqrt(h) 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 sqrt(h) 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

M3 - Working paper

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

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -