A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications

Area of Science:

• Statistics
• Econometrics
• Chemical Engineering

Background:

• Multicollinearity poses challenges in linear regression, affecting model stability and parameter estimation.
• Ridge regression and Liu-type estimators are established shrinkage methods to address multicollinearity.
• Existing methods have limitations in certain scenarios, necessitating new approaches.

Purpose of the Study:

• To propose a new shrinkage estimator for linear regression models to mitigate multicollinearity.
• To theoretically and empirically evaluate the performance of the new estimator.
• To compare the proposed estimator against established ridge and Liu estimators.

Main Methods:

• Development of a novel shrinkage estimator for linear regression.
• Theoretical analysis of the estimator's properties.
• Monte Carlo simulations to assess performance under varying conditions.
• Application to real-world chemical and economic datasets.

Main Results:

• The proposed estimator demonstrates improved performance in terms of mean squared error (MSE) under specific conditions.
• Simulation results show the new estimator outperforms both Liu and ridge regression estimators.
• Analysis of real-life data validates the practical applicability and effectiveness of the proposed method.

Conclusions:

• The new shrinkage estimator offers a valuable alternative for addressing multicollinearity in linear regression.
• The findings suggest the proposed method provides a more accurate and stable estimation in the presence of multicollinearity.
• The study contributes a novel technique with demonstrated advantages in both theoretical and practical settings.