SOME NEW GENERALIZED RIDGE REGRESSION ESTIMATORS

Abstract

Generalized Ridge regression (GRR) estimators have been identified to be more efficient than the Ordinary Least Square (OLS) estimator in the presence of Multicollinearity. In this research work, the concept of different forms on the basis of original, minimum, maximum and measures of locations of XIX of eigen values of Linear regression model resulted into some proposed GRR estimators. Three new GRR estimators in their original and different forms were also proposed. Investigation of the proposed and existing GRR estimators were done by conducting Monte Carlo experiments 5000 times on two linear regression models (p = 3 and p = 6) under six (6) levels of multicollinearity (= 0.8, 0.9, 0.95, 0.99, 0.999, 0.9999), three (3) levels of standard error (σ = 1, 5 and 10) and seven (7) levels of sample sizes (n = 10, 20, 30, 50, 100, 150, 250). The estimators were compared using Mean Square Error (MSE) criterion. Results showed that the proposed GRR estimators performed better than the existing GRR estimators in most cases, and that only one of the existing estimators is among the best seven (7) GRR estimators preferred. The overall best GRR estimator is a newly proposed one.