Robust variable selection through MAVE

Dimension reduction and variable selection play important roles in high dimensional data analysis. The sparse MAVE, a model-free variable selection method, is a nice combination of shrinkage estimation, Lasso, and an effective dimension reduction method, MAVE (minimum average variance estimation). However, it is not robust to outliers in the dependent variable because of the use of least-squares criterion. A robust variable selection method based on sparse MAVE is developed, together with an efficient estimation algorithm to enhance its practical applicability. In addition, a robust cross-validation is also proposed to select the structural dimension. The effectiveness of the new approach is verified through simulation studies and a real data analysis.