Abstract
<jats:p>Multicollinearity and heteroscedasticity are common problems in linear regression analysis that can adversely affect the stability, precision, and efficiency of parameter estimates. Although the generalised Liu-type estimator is useful for reducing the effect of multicollinearity, its performance depends largely on the appropriate selection of its shrinkage parameters. This study developed and evaluated improved generalised Liu-type estimators by modifying the shrinkage parameters (k) and (d) of the existing generalised two-parameter Liu estimator. Three improved parameter combinations, namely (k1d1), (k2d2), and (k3d3), were proposed and assessed using their mean square error properties. A Monte Carlo simulation study with 1,000 replications was conducted using sample sizes of (n=10, 20, 30, 50, 75,100), correlation levels ranging from (ρ = 0.7, 0.75 0.8, 0.85, 0.9, 0.95, 0.99) different error variances, and varying levels of heteroscedasticity. The performance of the estimators was evaluated using the mean square error (MSE) criterion and ranking procedure. The results showed that the improved estimators generally outperformed the original generalised Liu-type estimators in small and moderate sample sizes. In particular, the (k2d2), improvement based on 1/(Max(VIFs )) frequently produced the minimum mean square error under moderate and severe multicollinearity. The (k3d3) improvement was particularly useful in very small samples, whereas the original estimators remained competitive under extremely high multicollinearity and large sample sizes. The Portland Cement data application supported the simulation findings, with the second improvement emerging as the best overall alternative. The study concludes that the proposed improved generalised Liu-type estimators provide useful alternatives for regression models affected by multicollinearity and heteroscedasticity.</jats:p>