A COMPARATIVE STUDY OF THE PERFORMANCES OF THE PRINCIPAL COMPONENT RIDGE AND PRINCIPAL COMPONENT LIU ESTIMATORS USING DIFFERENT FORMS OF BIASING PARAMETER

Multicollinearity is a significant issue in multiple linear regression that occurs when two or more independent variables are highly correlated.This correlation undermines the reliability and stability of regression estimates, making it challenging to isolate and interpret the individual effect of each predictor variable.In the presence of multicollinearity, traditional estimation methods like Ordinary Least Squares (OLS) become less effective, often resulting in inflated standard errors and less reliable statistical inference.When multicollinearity exists, biased estimation techniques such as Ridge regression, the Liu estimator, and Principal Component-based estimators are frequently used.These estimators provide more stable and interpretable results when independent variables are correlated.Other estimators that are a combination of existing estimators have been formed.These include the Principal Component Ridge (PCRE) and Principal Component Liu (PCLIU) estimators.They further mitigate the adverse effects of multicollinearity.This study evaluates the performance of PCRE and PCLIU estimators under varying degrees of multicollinearity, sample sizes, and error variances.Seven distinct forms of the biasing parameter k, along with their generalized versions, are examined in this analysis.Originally introduced in 2019 by Fayose and Ayinde, these forms include the maximum, minimum, arithmetic mean, geometric mean, harmonic mean, mid-range, and median.Monte Carlo simulations, repeated 1,000 times, were conducted on regression models with four and seven predictors, across five levels of multicollinearity, three error variances, and eight sample sizes.The Mean Square Error (MSE) criterion was used for evaluation.Results indicate that the maximum form of the Principal Component Ridge estimator consistently outperforms others in terms of efficiency.