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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 nonrobustness property of the LS estimator.
Zahid Khan, , Katrina Lane Krebs, Sarfraz Ahmad, Aamir Saghir, Serpil Gumusteki. (2019) A New Modification of the Least Squares Method with Real Life Applications, Punjab University Journal of Mathematics, Volume 51, Issue 10.
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