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Mathematics
Volume 13
Issue 22
10.3390/math13223733
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Shrinkage Approaches for Ridge-Type Estimators Under Multicollinearity

by
Marwan Al-Momani
1,*,
Bahadır Yüzbaşı
2,
Mohammad Saleh Bataineh
1,
Rihab Abdallah
1 and
Athifa Moideenkutty
1
1
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates
2
Department of Econometrics, Inonu University, Malatya 44280, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(22), 3733; https://doi.org/10.3390/math13223733 (registering DOI)
Submission received: 6 October 2025 / Revised: 6 November 2025 / Accepted: 18 November 2025 / Published: 20 November 2025
(This article belongs to the Special Issue Advances in Statistical Methods with Applications)
Versions Notes

Abstract

Multicollinearity is a common issue in regression analyses that occurs when some predictor variables are highly correlated, leading to unstable least squares estimates of model parameters. Various estimation strategies have been proposed to address this problem. In this study, we enhanced a ridge-type estimator by incorporating pretest and shrinkage techniques. We conducted an analytical comparison to evaluate the performance of the proposed estimators in terms of their bias, quadratic risk, and numerical performance using both simulated and real data. Additionally, we assessed several penalization methods and three machine learning algorithms to facilitate a comprehensive comparison. Our results demonstrate that the proposed estimators outperformed the standard ridge-type estimator with respect to the mean squared error of the simulated data and the mean squared prediction error of two real data applications.
Keywords: ridge-type estimation; shrinkage; pretest; penalization methods; machine learning ridge-type estimation; shrinkage; pretest; penalization methods; machine learning

Share and Cite

MDPI and ACS Style

Al-Momani, M.; Yüzbaşı, B.; Bataineh, M.S.; Abdallah, R.; Moideenkutty, A. Shrinkage Approaches for Ridge-Type Estimators Under Multicollinearity. Mathematics 2025, 13, 3733. https://doi.org/10.3390/math13223733

AMA Style

Al-Momani M, Yüzbaşı B, Bataineh MS, Abdallah R, Moideenkutty A. Shrinkage Approaches for Ridge-Type Estimators Under Multicollinearity. Mathematics. 2025; 13(22):3733. https://doi.org/10.3390/math13223733

Chicago/Turabian Style

Al-Momani, Marwan, Bahadır Yüzbaşı, Mohammad Saleh Bataineh, Rihab Abdallah, and Athifa Moideenkutty. 2025. "Shrinkage Approaches for Ridge-Type Estimators Under Multicollinearity" Mathematics 13, no. 22: 3733. https://doi.org/10.3390/math13223733

APA Style

Al-Momani, M., Yüzbaşı, B., Bataineh, M. S., Abdallah, R., & Moideenkutty, A. (2025). Shrinkage Approaches for Ridge-Type Estimators Under Multicollinearity. Mathematics, 13(22), 3733. https://doi.org/10.3390/math13223733

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