Robust signed-rank estimation and variable selection for semi-parametric additive partial linear models

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Parametric models struggle with unknown functional forms or error distributions.
• Outliers and unusual observations pose significant challenges to standard modeling techniques.
• Robust model selection is crucial when covariates and functional form smoothness are uncertain.

Purpose of the Study:

• To develop a robust model selection and estimation approach for semi-parametric additive models.
• To address challenges posed by unknown functional forms, error densities, and data contamination.
• To provide a reliable tool for analyzing complex datasets, including those with outliers.

Main Methods:

• Utilizing weighted signed-rank estimation for robustness.
• Employing the adaptive lasso for variable selection in semi-parametric models.
• Estimating unknown additive nonparametric functions using B-spline techniques.

Main Results:

• The proposed weighted signed-rank estimation with adaptive lasso demonstrates an oracle property.
• The method proves robust against heavy-tailed errors, data contamination, and high-leverage points.
• Simulations confirm the effectiveness and robustness of the approach.

Conclusions:

• The developed method offers a powerful and robust solution for semi-parametric modeling.
• It effectively handles complex data structures and potential outliers.
• The approach is validated through simulations and a practical application in economic analysis.