Review of Some Robust Estimators in Multiple Linear Regressions in the Presence of Outlier(s)

Abstract

Linear regression has been one of the most important statistical data analysis tools. Multiple regression is a type of regression where the dependent variable shows a linear relationship with two or more independent variables. OLS estimate is extremely sensitive to unusual observations (outliers), with low breakdown point and low efficiency. This paper reviews and compares some of the existing robust methods (Least Absolute Deviation, Huber M-Estimator, Bisquare M-Estimator, MM Estimator, Least Median Square, Least Trimmed Square, S-Estimator); a simulation method is used to compare the selected existing methods. It was concluded based on the results that for y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.3 is MM; for x direction outlier, the best estimator in term breakdown point of at most 0.4 is S; for x, y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.2 is MM.