A simulation study of the robustness of the least median of squares estimator of slope in a regression through the origin model

Date

2010-12-17

Journal Title

Journal ISSN

Volume Title

Publisher

Kansas State University

Abstract

The principle of least squares applied to regression models estimates parameters by minimizing the mean of squared residuals. Least squares estimators are optimal under normality but can perform poorly in the presence of outliers. This well known lack of robustness motivated the development of alternatives, such as least median of squares estimators obtained by minimizing the median of squared residuals. This report uses simulation to examine and compare the robustness of least median of squares estimators and least squares estimators of the slope of a regression line through the origin in terms of bias and mean squared error in a variety of conditions containing outliers created by using mixtures of normal and heavy tailed distributions. It is found that least median of squares estimation is almost as good as least squares estimation under normality and can be much better in the presence of outliers.

Description

Keywords

Least median of squares estimates, Regression, Estimates, Median, Regression through the origin

Graduation Month

December

Degree

Master of Science

Department

Department of Statistics

Major Professor

Paul I. Nelson

Date

2010

Type

Report

Citation