Two New Ridge Parameters and A Guide for Selecting an Appropriate Ridge Parameter in Linear Regression

Abstract

The ridge regression estimator was first introduced by Hoerl and Kennard [6] as an alternative method to the ordinary least squares (OLS) estimator when multicollinearity exists among regressors. Ridge regression depends on the estimation of the ridge parameter presented in this study as k. On the other hand there is not a standard way of determining k. In the literature, there are a lot of proposed ridge parameters. The aim of this paper is to introduce two new ridge parameters and make comparison of 37 different ridge parameters including the proposed ones. A simulation study has been conducted to make comparisons in terms of the mean square error criterion. It is found that the proposed ridge parameters produce better results than most of the other parameters. The parameters proposed by Asar et. al. [2] very recently did not perform as well as their results. In fact, the parameters we have proposed did perform much better than theirs in every single case. However, there is no explicit ridge parameter that performs well in every situation. The ridge estimators act differently in various sample sizes, dimensions and collinearity degrees. We think that this study is helpful for researchers employing ridge regression as they may use the comparative results provided in the study to make a decision of choosing the best ridge parameter for their case.