A New Modification of the Least Squares Method with Real Life Applications

Abstract

A new regression M-estimator namely modified least squares (MLS) in the class of M-estimators is presented in this study. The proposed estimator overcomes the non-robustness property associated with traditional approach of the least square (LS) estimator. The effectiveness of the loss function used for proposed estimator has been compared with that of commonly implemented approach of the LS estimator. The influence and weight functions have been derived to analyze the robustness of the proposed estimator against the polluted measurements. Real data examples in statistical applications have been used to analyze the effectiveness of proposed estimator. The empirical results from real applications also confirm that MLS estimator substantially enhances the non-robustness property of the LS estimator.