Improving Corrected Modified Unbiased Ridge Regression Estimator in the Linear Regression Model With Correlated Errors

This study introduces a novel bias estimator within the linear regression framework, specifically addressing models with correlated or heterogeneous errors. Recognizing the limitations of traditional estimation methods like Ordinary Least Squares (OLS) in the presence of multicollinearity and autocorrelated errors, the proposed estimator provides a robust alternative by leveraging bias corrections. The new estimator, termed Corrected Modified Unbiased Ridge Regression (CMURR), incorporates two parameters, 𝑘 and 𝑑, to enhance accuracy. The properties of CMURR are derived, including its mean squared error (MSE), which serves as a key metric for performance evaluation. The CMURR estimator is rigorously compared against existing estimators, including the Modified Almost Unbiased Liu Estimator (MAULE), the Modified Almost Unbiased Two-Parameter Estimator (MAUTP), and the Mustafa Unbiased Ridge Regression (MURR). Simulation studies, conducted under varying degrees of multicollinearity and heteroscedasticity, demonstrate the superior performance of CMURR in reducing MSE across diverse conditions. Additionally, a numerical example utilizing real-world data from economic indicators underscores its practical applicability. Results indicate that the proposed estimator consistently outperforms others, particularly in scenarios involving high multicollinearity or correlated errors. The findings contribute to the ongoing advancement of statistical methods in regression analysis, providing a reliable tool for researchers handling complex error structures in data.