A Robust Fast Greedy Model Averaging Method for High-Dimensional Regression with Outliers

In this paper, we investigate robust model averaging for high-dimensional data with outlier contamination. Most existing model averaging methods rely on ordinary least squares (OLS) estimation and are therefore highly sensitive to outliers. Moreover, these methods are generally not designed to accommodate high-dimensional settings. To overcome these limitations, we propose a robust fast greedy model averaging (Robust FGMA) method. The proposed approach incorporates the Huber robust loss function and fold-specific median absolute deviation (MAD) scale estimation into the cross-validation weight-selection criterion within the fast greedy model averaging (FGMA) framework. Simulation studies demonstrate that Robust FGMA achieves superior predictive accuracy and stability under various contamination and high-dimensional scenarios. Furthermore, empirical analysis based on the real biological dataset GSE10245 supports the effectiveness of the proposed method in the presence of outliers. The proposed approach retains the accelerated weight optimization structure of FGMA and is applicable to high-dimensional regression settings.