Modified Liu estimators in the linear regression model: An application to Tobacco data

Area of Science:

• Statistics
• Econometrics

Background:

• Multicollinearity in multiple linear regression inflates ordinary least squares estimator variance.
• Liu regression offers a biased estimation method using a shrinkage parameter 'd' to address multicollinearity.
• Optimal shrinkage parameter selection is crucial for balancing bias and variance.

Purpose of the Study:

• To propose novel shrinkage parameter estimators for Liu regression.
• To evaluate the performance of these new estimators against existing ones.
• To demonstrate the practical utility of the proposed estimators using a real-world dataset.

Main Methods:

• Development of new shrinkage parameter estimators based on regression coefficient quantiles.
• Performance evaluation using Monte Carlo simulations with Mean Squared Error (MSE) and Mean Absolute Error (MAE).
• Application to the Tobacco dataset for assessing prediction intervals.

Main Results:

• The proposed estimators demonstrate superior performance over existing methods, particularly in scenarios with high multicollinearity.
• The new estimators yield the best 95% mean prediction intervals for the Tobacco dataset.
• Simulation results confirm the effectiveness of the new estimators in reducing MSE and MAE.

Conclusions:

• The newly developed shrinkage parameter estimators are recommended for practical use in the presence of high to severe multicollinearity.
• These estimators offer improved bias-variance trade-offs and prediction accuracy.
• The findings provide valuable tools for robust regression analysis in econometrics and statistics.