The Comparing of S-estimator and M-estimators in linear regression

Abstract

In the presence of outliers, least squares estimation is inefficient and can be biased. In the 1980’s several alternatives to M-estimation were proposed as attempts to overcome the lack of resistance. Least Trimmed Squares (LTS) is a viable alternative and is presently the preferred choice of Rousseeuw and Ryan (1997, 2008). Another proposed solution was S-estimation. This method finds a line that minimizes a robust estimate of the scale of the residuals. This method is highly resistant to leverage points, and is robust to outliers in the response. However, this method was also found to be inefficient.

 

The aim of this study is to compare S-estimator with other robust estimators and the least squares estimators and also an example is given to illustrate the efficiency of S-estimator. The data used in this example are the air pollution measures. And finally a simulation study has been presented in this study.

 

Key words: M-estimators, S-estimator, Robust regression, Least median squares ,Air pollution

 

Keywords

• M-estimators, S-estimator, Robust regression, Least median squares ,Air pollution