A MODIFIED BIASING RIDGE ESTIMATORS FOR ADDRESSING MULTICOLLINEARITY PROBLEM IN LINEAR REGRESSION MODEL

Abstract

This study conduct an extensive analysis of various biasing estimators in the context of multiple
explanatory variable (p) and varying degree of multicollinearity, a number of approaches have
been developed for deriving biasing estimators. In this study, a new approach to obtain the ridge
biasing parameter k is suggested and then evaluated by Monte Carlo simulations. A number of
different models are investigated for different number of observations, the strength of correlation
between the explanatory variables, and distribution of the error terms. The mean squared error
(MSE) criterion is used to examine the performance of the proposed estimators when compared
with other well-known estimators. Accordingly, the analysis revealed that generally, mean
square error (MSE) value of the estimators decrease as the degree of correlation among
explanatory variables increased with a few exceptions. In conclusion, kibria’s biasing estimator
proposed in 2022 exhibit effectiveness across multicollinearity level, error terms, sample sizes
and correlation levels. These results provide valuable insight for researcher and practitioner
seeking to choose appropriate biasing estimators in similar statistical scenarios.