Improving the Performance of the Andrews Weighted Function in a Robust Multiple Linear Regression Model

Outliers affect the accuracy of estimating multiple linear regression model parameters and lead to estimated parameters that are inaccurate and far from their true values; thus, robust estimator methods such as the Andrews weighted function must be used to obtain more accurate parameters and robustness versus outliers. The proposed method involves choosing the optimal tuning parameter value that produces the minimum mean square error of the parameters and treating outliers. Simulation and real data were used to compare the efficiency of the models estimated based on the classical robust method for Andrews weighted function that uses the default tune parameter and the proposed algorithm through the MATLAB program dedicated to this purpose. The research results revealed the efficiency of the proposed algorithm in estimating optimal tuning parameters for the Andrews weighted function and treating outliers and the accuracy of estimating the model parameters.