A modified partial robust M-regression to improve prediction performance for data with outliers

This paper introduces a modified partial robust M-regression approach. The objective of the new approach is to improve the prediction accuracy of the regression model for data containing outliers. The original PRM is an efficient robust linear regression method which is devoting to down-weighting the outliers by choosing proper weighting scheme with relatively less computational load. Although PRM shows superior performance compared to the existing approaches, it fails to make all the residual weights for outlier coverage to zeros within the iteration steps, which indicates the calculated regression model may be still affected by these outliers. Based on a novel distance measurement method and a corresponding center estimate method, a modified partial robust M-regression approach called mPRM is presented to overcome the drawback of PRM. Simulation study shows that the new approach not only inherits the robustness and efficiency of PRM, but also has a more accurate prediction performance than PRM.