Bootstrap-quantile ridge estimator for linear regression with applications.

Area of Science:

• Statistics
• Econometrics
• Data Analysis

Background:

• Ordinary least squares regression struggles with collinear predictors.
• Ridge regression offers a solution using a biasing parameter.
• Bootstrap methods provide robust estimation through resampling.

Purpose of the Study:

• To develop a nonparametric bootstrap-quantile approach for estimating the ridge parameter in linear regression.
• To enhance the performance of ridge regression estimators, particularly in the presence of multicollinearity.
• To provide a more accurate and reliable estimation method for collinear data analysis.

Main Methods:

• Development of a nonparametric bootstrap-quantile estimation technique.
• Application of the method to popular ridge regression estimators.
• Comparison with baseline ridge estimators using Monte Carlo simulations.
• Validation through application to real-world datasets.

Main Results:

• The proposed bootstrap-quantile approach yields substantially smaller Mean Squared Errors (MSE) compared to baseline ridge estimators.
• Performance improvements are most significant in datasets with high collinearity among predictors.
• Empirical evidence from simulations and real data applications supports the method's effectiveness.

Conclusions:

• The bootstrap-quantile approach is a superior method for estimating ridge parameters in linear regression, especially under high collinearity.
• This technique offers improved accuracy and reliability for analyzing datasets with multicollinear predictors.
• The method demonstrates practical utility and suitability for real-world data analysis.