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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 1

Novel heteroscedastic robust ridge M-estimators for linear regression model

Hina Naz(Quaid-i-Azam University)0009-0006-7477-975X
Ismail Shah(University of Padova)0000-0001-5005-6991
Danish Wasim(Abasyn University Peshawar)0000-0002-9620-8855
Sajid Ali(Quaid-i-Azam University)0000-0003-4868-7932
Pages
—
Publication Date
2026-02-02
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, real-world applications validate the potential of this methodology as a valuable tool for data analysis in scenarios characterized by collinear predictors and heteroscedastic errors.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Penalized regression techniques are widely used when the number of predictors is large and they are highly inter-correlated.
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Key Findings & Data:This new approach improves the performance of ridge estimators compared to traditional techniques.
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Conclusion & Impact:Furthermore, real-world applications validate the potential of this methodology as a valuable tool for data analysis in scenarios characterized by collinear predictors and heteroscedastic errors.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Heteroscedastic ridge regression · multicollinearity · mean squared error

Abstract

Penalized regression techniques are widely used when the number of predictors is large and they are highly inter-correlated. Within penalized linear regression techniques, ridge regression is primarily used to obtain estimators that minimize the mean squared error while fitting the regression model. This research work addresses the issue of ridge estimation when multicollinearity, heteroscedasticity, and outliers exist within the predictors. For example, in a dataset that predicts livestock production based on factors such as animal population and feed quality, an outlier, such as an unusually high number of livestock in one region due to a large farm, could distort the regression results. To this end, we introduced a novel heteroscedastic ridge M-estimator approach in conjunction with the scaling factor method. This new approach improves the performance of ridge estimators compared to traditional techniques. To demonstrate its effectiveness, the proposed methodology is compared with several widely used and latest ridge estimators. Extensive simulations demonstrate the remarkable performance of the proposed approach, particularly in the presence of severe multicollinearity, heteroscedasticity, and outliers. Furthermore, real-world applications validate the potential of this methodology as a valuable tool for data analysis in scenarios characterized by collinear predictors and heteroscedastic errors.

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Cite This Article

Naz, H., Shah, I., Wasim, D., Ali, S. (2026). Novel heteroscedastic robust ridge M-estimators for linear regression model. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 1. https://doi.org/10.15672/hujms.1734907

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