REDESCENDING M-ESTIMATOR FOR ROBUST REGRESSION
In the linear regression problem, redescending M-estimators are used as an alternative method to the ordinary least square method when there are outliers in the data. Using the nonlinear transformations on the data one cannot remove the effect of outliers completely. In this paper, a redescending estimator is introduced for the robust regression to remove the effect of outliers in the data. The proposed estimator rejects the effect of outliers and provides efficient results about the parameter. The Ψ-function of the proposed objective function attains more linearity in the center before it redescends as compared to Insha (2006), Tukey (1974), Qadir (1996) and Andrews et al. (1972). The weight function of the proposed redescending M-estimator also gives improved results for the purpose it is introduced. To evaluate the prescribed results, a simulation study is conducted. A real data application is presented to demonstrate the performance of proposed estimator.