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 e ffi ciency. This paper reviews and compares some of the existing robust methods (Least Absolu te 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 o utlier, 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 effici ency and breakdown point of at most 0.2 is MM.