IMPROVING CORRECTED MODIFIED UNBIASED RIDGE REGRESSION ESTIMATOR IN THE LINEAR REGRESSION MODEL WITH CORRELATED ERRORS

AL-Dulaimi, Mustafa M. Abdullah; Alheety, Mustafa I.

doi:10.63298/asj.2025.185252

	IMPROVING CORRECTED MODIFIED UNBIASED RIDGE REGRESSION ESTIMATOR IN THE LINEAR REGRESSION MODEL WITH CORRELATED ERRORS
Anbar Science Journal
Volume 1, Issue 1, February 2025, Pages 31-44 PDF (878.63 K)
Document Type: Original Article
DOI: 10.63298/asj.2025.185252
Authors
Mustafa M. Abdullah AL-Dulaimi; Mustafa I. Alheety^*
Department of Mathematics, College of education for pure science, University Of Anbar, Anbar, Iraq
Abstract
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.
Highlights
Introduces a new bias estimator (CMURR) for linear regression models with correlated and heterogeneous errors. Addresses limitations of traditional estimators like Ordinary Least Squares (OLS) in handling multicollinearity and autocorrelation. Proposes a two-parameter correction (k and d) to improve estimation accuracy and minimize mean squared error (MSE). Demonstrates superior performance of CMURR through simulation studies and comparison with MAULE, MAUTP, and MURR estimators. Validates the estimator using real-world economic data, showcasing its practical applicability in complex regression models.
Keywords
Bias Estimation; Ridge Regression; Multicollinearity; Mean Squared Error; Heteroscedasticity; Correlated Errors

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