Robust-stein estimator for overcoming outliers and multicollinearity

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Ordinary least squares (OLS) estimators are negatively impacted by correlated regressors.
• Existing robust methods like M-estimators combined with ridge estimators address outliers and collinearity but not simultaneously.
• Stein and ridge estimators improve accuracy but lack robustness to outliers.

Purpose of the Study:

• To introduce a novel robust Stein estimator.
• To address issues of correlated regressors and outliers in linear regression models simultaneously.
• To evaluate the performance of the proposed robust Stein estimator against existing methods.

Main Methods:

• Development of a robust Stein estimator.
• Conducting simulation studies to compare estimator performance.
• Applying the estimator to a real-world dataset.

Main Results:

• The proposed robust Stein estimator demonstrates favorable performance.
• The new technique effectively handles both correlated regressors and outliers.
• Simulation and application results show superiority over existing methods.

Conclusions:

• The robust Stein estimator is a valuable tool for linear regression with correlated regressors and outliers.
• The proposed method offers improved estimation accuracy and robustness.
• This technique provides a more reliable alternative to traditional and existing robust methods.