Ridge-Type MML Estimator in the Linear Regression Model

Abstract

Ridge regression is widely used to deal with the multicollinearity problem. However, traditional ridge estimator (Hoerl and Kennard 1970) loses its efficiency in the presence of outliers, since it is obtained based on least squares (LS) estimation. Therefore, Silvapulle (1991) proposes ridge-type M-estimator to cope with the problems imposed by outliers. In this study, we also propose a new ridge-type estimator by following the similar lines as in Silvapulle (1991). However, here we use a modified maximum likelihood (MML) estimator instead of an M-estimation, because they are robust to outliers and at least as good as M-estimators when the error distribution is modeled as long-tailed symmetric (LTS). The proposed estimator is called as ridge-type MML estimator since it is obtained based on MML estimator. We conduct a Monte-Carlo simulation study to compare the performance of the proposed estimator with the traditional ridge estimator and ridge-type M-estimator. It is seen that proposed estimator outperforms its rivals in terms of the mean square error (MSE) criterion. Real life data is also considered to show the implementation of the proposed estimator.