A redescending M-estimator approach for outlier-resilient modeling

The OLS model is built on the assumption of normality in the distribution of error terms. However, this assumption can be easily violated, especially when there are outliers in the data. A single outlier can disrupt the normality assumption of error terms, making the OLS model less effective. In such situations, M-estimators (MEs) come into play to obtain reliable estimates. We introduce a redescending M-estimators (RME) for robust regression to handle datasets with outliers. The proposed RME produces more robust estimates by effectively managing the influence of outliers, even at lower values of the tuning constant. We compared the performance of this estimator with existing RMEs using real-life data examples and an extensive simulation study. The results show that our suggested RME is more efficient than the compared ME in various situations.