Graphical evaluation of the ridge-type robust regression estimators in mixture experiments

Area of Science:

• Statistics
• Experimental Design
• Chemometrics

Background:

• Ordinary least squares (OLS) is standard for parameter estimation in mixture experiments.
• OLS performance degrades significantly with multicollinearity and outliers.
• Combined multicollinearity and outliers pose a substantial challenge in mixture analysis.

Purpose of the Study:

• To evaluate ridge-type robust estimators for mixture experiments.
• To address parameter estimation issues caused by multicollinearity and outliers.
• To introduce a graphical method for selecting optimal ridge-type robust estimators.

Main Methods:

• Investigated various ridge-type robust regression estimators.
• Employed fraction of design space plots for biasing parameter selection.
• Assessed estimator performance based on scaled mean squared error of prediction.

Main Results:

• Ridge-type robust estimators demonstrate potential in mitigating OLS limitations.
• The fraction of design space plots effectively guide the selection of biasing parameters.
• The proposed graphical approach provides a practical tool for analyzing mixture data.

Conclusions:

• Ridge-type robust estimators offer a viable alternative to OLS in challenging mixture experiments.
• The graphical selection method enhances the reliability of parameter estimation.
• The study provides a practical framework for robust analysis of mixture data with outliers and multicollinearity.