A New Mixed Biased Estimator for Ill-Conditioning Challenges in Linear Regression Model With Chemometrics...

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Ordinary Least Squares (OLS) is standard for linear regression but struggles with non-orthogonal models.
• Non-orthogonal models can yield unreliable regression coefficient estimates using OLS.

Purpose of the Study:

• Introduce a novel mixed-biased estimator for enhanced linear regression in non-orthogonal scenarios.
• Address the limitations of existing estimators like OLS, Stein, and ridge in specific model conditions.

Main Methods:

• The proposed estimator combines Stein and ridge estimators.
• Theoretical properties were analyzed, and shrinkage parameter estimation methods were proposed.
• Performance was evaluated against OLS, Stein, and various ridge estimators using Mean Squared Error (MSE).

Main Results:

• Simulation studies demonstrated the proposed estimator's superiority.
• Practical applications using cement and crock datasets confirmed its enhanced performance.
• The novel estimator consistently outperformed traditional methods in MSE criteria.

Conclusions:

• The new mixed-biased estimator offers a more reliable alternative for non-orthogonal linear regression.
• It provides improved estimation accuracy compared to OLS, Stein, and ridge estimators.
• The findings are validated through both simulated data and real-world datasets.