Robust model averaging approach by Mallows-type criterion.

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Model averaging is crucial for managing model selection uncertainty and integrating information from multiple models.
• Existing methods often rely on ordinary least squares or maximum likelihood, making them sensitive to outliers and assumption violations.
• Optimal robust methods for mean regression model averaging are lacking.

Purpose of the Study:

• To develop an outlier-robust model averaging approach for mean regression.
• To provide a trustworthy statistical analysis method resilient to data contamination.
• To address the limitations of existing model averaging techniques.

Main Methods:

• Proposed an outlier-robust model averaging approach using a Mallows-type criterion.
• Constructed generalized M (GM) estimators for candidate models.
• Developed robust weighting schemes based on the asymptotic expansion of final prediction error using a GM-type loss function.

Main Results:

• Established asymptotic properties of the proposed robust model averaging estimators.
• Derived the consistency of weight estimators converging to optimal weight vectors.
• Demonstrated the robustness of the model averaging estimator through a bounded influence function.
• Defined an empirical prediction influence function for quantitative robustness evaluation.

Conclusions:

• The proposed method offers a reliable solution for model averaging in the presence of outliers.
• The approach maintains trustworthy results even with contaminated response and/or covariate data.
• Simulation studies and real data analysis confirm the effectiveness and robustness of the new estimators.