Akhtar Nadeem, Alharthi Muteb Faraj
Government Degree College Achin Payan Higher Education Department, Peshawar, Khyber Pakhtunkhwa, Pakistan.
Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia.
Sci Rep. 2025 Mar 28;15(1):10774. doi: 10.1038/s41598-025-94857-7.
In this study, we introduce three new shrinkage parameters for ridge regression, which dynamically adjust the ridge penalty based on the properties of the data, particularly the multicollinearity structure. Using these new parameters, we develop three ridge condition-adjusted estimators (CAREs), referred to as CARE1, CARE2, and CARE3, which specifically designed to enhance predictive accuracy in datasets with significant multicollinearity and high error variance. The performance of the developed shrinkage estimators is rigorously evaluated through extensive simulation studies, using the Mean Square Error (MSE) criterion for accuracy assessment. The simulation results reveal that our proposed estimators consistently outperform existing estimators under different scenarios. We also apply these estimators to a real-world dataset to demonstrate their practical effectiveness, thereby showcasing their applicability in real-life data analysis. The real-world application further validates their practical utility for accurate prediction and model stability in complex scenarios in which the CARE3 emerged as the best-performing shrinkage estimator.
在本研究中，我们为岭回归引入了三个新的收缩参数，这些参数根据数据的特性，特别是多重共线性结构，动态调整岭惩罚。使用这些新参数，我们开发了三种岭条件调整估计器（CAREs），分别称为CARE1、CARE2和CARE3，它们专门设计用于提高具有显著多重共线性和高误差方差的数据集中的预测准确性。通过广泛的模拟研究，使用均方误差（MSE）准则进行准确性评估，对所开发的收缩估计器的性能进行了严格评估。模拟结果表明，我们提出的估计器在不同场景下始终优于现有估计器。我们还将这些估计器应用于一个真实世界的数据集，以证明它们的实际有效性，从而展示它们在实际数据分析中的适用性。实际应用进一步验证了它们在复杂场景中进行准确预测和模型稳定性的实际效用，其中CARE3成为表现最佳的收缩估计器。
