Subset Selection in Linear Regression Using Generalized Ridge Estimator

Abstract

In multiple regression model multicollinearity is a common problem that produces undesirable effects on the least squares estimator. Consequently, subset selection methods such as Mallows’ C_p, which are based on least squares estimates lead to select a ‘wrong’ subset. To overcome the problem due to multicollinearity a new subset selection method based on generalized ridge estimator is proposed. We have shown that proposed subset selection method is a better alternative compound to the methods, which are based on least squares estimator when the data exhibits multicollinearity. We have evaluated performance of the proposed method through the simulation study. The novel feature of the proposed method is that it can be used with least squares estimator or generalized ridge estimator of β without any modification in the proposed statistic.