Abstract
M-estimators are robust estimators that give less weight to the observations that are outliers while redescending M-estimators are those estimators that are built such that extreme outliers are completely rejected. In this paper, redescending M-estimators are compared using both the Monte Carlo simulation method and the real life data to ascertain the method that is more efficient and robust when outliers are in both x and y directions. The results from the simulation study and the real life data indicate that Anekwe redescending M-estimator is more efficient and robust when outliers are in both x and y directions.
Highlights
[4] proposed Tukey’s biweight M-estimator and its -function is given as
At 20% outliers in both axes in a simple regression as shown in Table 3, the Anekwe and Alarm estimators are more efficient and robust compared to other estimators
We applied the redescending M-estimators to real-life data and the dataset had been extensively used by other researchers in the area of robust regression
Summary
[4] proposed Tukey’s biweight M-estimator and its -function is given as [1] proposed the Alarm’s Redescending M-estimator for robust regression and outlier detection. Its -function is given as where is the tuning constant and are the residuals scaled over MAD.
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