Performance of Some Modified Ordinary Ridge Regression Estimators

Abstract

In multiple linear regressions, if the data suffer from severe multicollinearity, then the ordinary least squares (OLS) method become more sensitive to it, and in such a case OLS could yield wrong sign for some of the regression coefficients. Therefore, when such a situation arises, we could use one of the biased regression methods viz., ridge regression (RR), principal component regression(PCR), etc., as an alternative method to OLS. This paper pertains to ridge regression only. To overcome the problem of multicollinearity, here we propose some modified ordinary ridge estimators, which are defined by taking convex combinations of some of the existing estimators. Empirically performance of the suggested estimators is compared with some of the existing estimators which are considered in this study, and the results indicate the suggested estimators performed better in terms of MSE. Moreover, the suggested estimators are more robust to problem of linear dependency between the predictors.