A Comparison of MM-estimation and Fuzzy Robust Regression for Multiple Regression Model with Outliers

Abstract

In this paper, MM-estimation and fuzzy robust regression, developed from M-estimation, are used for modelling and are compared the model performance by simulation the data sets containing outliers in X, outliers in Y and outliers in X and Y, respectively. The robust regression is considered by the estimated mean square error (EMSE) (or the mean square of the bias values) and the mean absolute error (MAE) values. These values indicate estimation precision. The fuzzy robust regression provides the models being more robust than the MM-estimation almost all types of outliers because it has a lower EMSE and MAE, especially, outliers in both X and Y. Nevertheless, the MM-estimation is more effective than the fuzzy robust regression for case of 30% of outliers in X when n = 20 and 40, respectively and case of 10% and 20% of outliers in Y.