More Efficient Methods among Commonly Used Robust Estimation Methods for Robust Unitary Linear Regression

Abstract

Robust regression, based on the robust estimation, can effectively eliminate or weaken the influences of outliers. However, different robust methods have different abilities to eliminate or weaken the influences of outliers. The current paper employs simulation experiments, taking unitary linear regressions with different numbers of observations, different numbers of gross errors and different values of gross errors as examples, to compare the robustness of 13 commonly used robust estimation methods by the average values of relative gains. The results indicate that the L1 and GermanMcClure methods are relatively more efficient for unitary linear regression. They can more efficiently eliminate or weaken the influences of gross errors on regression coefficient valuation than other robust estimation methods.