Adaptive Liu estimator modified for estimating regression coefficients in the presence of Multicollinearity

Multicollinearity among predictor variables remains a major challenge in regression analysis. This issue arises when predictors are highly correlated, leading to inflated variances of ordinary least squares (OLS) estimators and unstable coefficient estimates. Several remedial methods have been proposed to mitigate Multicollinearity, including ridge regression, the Liu estimator, and principal component regression. A critical factor determining the performance of shrinkage estimators such as the Liu estimator is the selection of an appropriate shrinkage parameter, denoted by $d$. This study proposes a novel method for estimating the optimal value of $d$. The performance of the proposed estimator was evaluated through Monte Carlo simulations under varying levels of {{Multicollinearity}} severity and sample size. The method was also applied to a real-world dataset. Results demonstrate that the proposed estimator achieves a substantially lower mean squared error ($MSE$) and mean absolute error ($MAE$) compared to existing estimators, indicating superior estimation accuracy and stability.