Enhancing performance in the presence of outliers with redescending M-estimators.

In real-life situations, we have to analyze the data that contains the atypical observations, and the presence of outliers has adverse effects on the performance of ordinary least square estimates. In this situation, redescedning M-estimators, proposed by Huber (1964), are used to tackle the effects of outliers to increase the efficiency of least square estimates. In this study, we introduce a redescending M-estimator designed to generate robust estimates by mitigating the influence of outlier observations, even when the tuning constant is set to low values. This innovative estimator exhibits enhanced linearity at its core and maintains continuity throughout its range. Our proposed estimator stands out for its novelty, simplicity, differentiability, and practical applicability across real-world scenarios. The results of the proposed redescedning M-estimators are compared with existing robust estimators using an extensive simulation study. Two examples based on real-life data are also added to validate the performance of the suggested function. The formulated redescedning M-estimator produced efficient results as compared to all the considered redescedning M-estimators.