Improving the Robustness of the Theil-Sen Estimator Using a Simple Heuristic-Based Modification

Abstract

One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators.