Some improved classification-based ridge parameter of Hoerl and Kennard estimation techniques

Abstract

In a linear regression model, it is often assumed that the explanatory variables are independent. This assumption is often violated and Ridge Regression estimator introduced by [2]has been identified to be more efficient than ordinary least square (OLS) in handling it. However, it requires a ridge parameter, K, of which many have been proposed. In this study, estimators based on Hoerl and Kennard were classified into different forms and various types and some modifications were proposed to improveit. Investigation were done by conducting 1000 Monte-Carlo experiments under five (5) levels of multicollinearity, three (3) levels of error variance and five levels of sample size. For the purpose of comparing the performance of the improved ridge parameter with the existing ones, the number of times the MSE of the improved ridge parameter is less than the existing ones is counted over the levels of multicollinearity (5) and error variance (3). Also, a maximum of fifteen (15) counts is expected. Results show that the improved ridge parameters proposed in this study are better than the existing ones.

Keywords: Linear Regression Model, Multicollinearity, Ridge Parameter Estimation
Techniques, Relative Efficiency