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Abstract:
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Dimension reduction and variable selection play important roles in high dimensional data analysis. Minimum Average Variance Estimation (MAVE) is an efficient approach among many others. However, because of the use of least squares criterion, MAVE is not robust to outliers in the dependent variable or errors with heavy tailed distributions. A robust extension of MAVE through modal regression is proposed. This new approach can adapt to different error distributions and thus brings robustness to the contamination in the response variable. The estimator is shown to have the same convergence rate as the original MAVE. The efficacy of this new solution is illustrated through simulation studies and a real data analysis.
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