American Review of Mathematics and Statistics

A Comparative Study of TELBS Robust Linear Regression
Hong Li, Wayne M. Eby

Abstract
Linear regression is a widely used statistical approach to model the relationship between a dependent variable and one or more independent variables. Regression parameters are often estimated using the method of ordinary least squares (OLS). Unfortunately, OLS estimates are very sensitive to outliers. Tabatabai et. al. [30] introduced TELBS robust linear regression method. TELBS estimates have high asymptotic efficiency and high breakdown point. In this study we use simulation to assess the performance of TELBS robust technique in comparison with other methods such as M estimate, MM estimate, S estimate, and Least Trimmed Square (LTS) estimate. We examine the presence of outliers in the direction of response variable, covariates direction, and in both the response and covariates direction. In addition, two real data sets are used to illustrate these methods. Some diagnostic measures are introduced and computed to identify the outliers. Results indicate that as the percentage of outliers increases, TELBS method outperforms other methods considered in this study.

Full Text: PDF     DOI: 10.15640/arms.v6n1a1