Applied Mathematics & Information Sciences

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The presence of Partial Robust M-Regression (PRM) amongst other Partial Least Squares Regression (PLSR) techniques is mainly to offer a more robust and efficient method than the existing ones when data face outlier problem. PRMis conceptually different from other robust PLSR techniques because it proposed the usage of M-estimator instead of a more commonly used Least Squares (LS) estimator. Recently, there are several efforts among researchers to further enhance the PRM performance. Among those methods are Partial Robust M-Regression (based on Bisquare Weight Function) (PRMBS) and Partial Robust M-Regression (based on Hampel Weight Function) (PRMH). These two methods are re-descending weight based PRMs which differ from the original monotonous weight based PRM. This study compares the performance of PLS, PRM, PRMBS and PRMH under numerous outlying conditions for both low and high dimensional data sets. Some analysis of real data sets and simulation results in this study show the robustness and the effectiveness of the modified PRM methods.

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