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Rekabdarkolaee, Hossein Moradi; Boone, Edward; Wang, Qin

Robust estimation and variable selection in sufficient dimension reduction. (English) Zbl 1466.62182

Comput. Stat. Data Anal. 108, 146-157 (2017).
Summary: 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. Furthermore, the proposed method is combined with adaptive LASSO to select informative variables. The efficacy of this new solution is illustrated through simulation studies and a data analysis on Hong Kong air quality.

Cited in 5 Documents

MSC:

62-08 Computational methods for problems pertaining to statistics

Keywords:

robust estimation; shrinkage estimation; sufficient dimension reduction; variable selection

Software:

glmnet
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Full Text: DOI

References:

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