Abstract
High dimensionality has been a significant feature in modern statistical modeling. Sufficient dimension reduction (SDR) as an efficient tool aims at reducing the original high dimensional predictors without losing any regression information. Minimum average variance estimation (MAVE) is a popular approach in SDR among others. However, it is not robust to outliers in the response due to the use of least squares. A robust estimation through regularization with case-specific parameters is proposed to achieve robust estimation and outlier detection simultaneously. Under the nonconvex penalized regression framework, two efficient computational strategies are introduced. Simulation studies and a real data application show the efficacy of the proposed approach. Compared with existing methods, the proposed approach is less sensitive to the choice of initial estimators.
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