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We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates.
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A. H. Welsh and E. Ronchetti · 2002
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J. Fan and H. Peng · 2004
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Robust Regression and Outlier Detection
P. J. Rousseeuw and A. M. Leroy · 2005
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Robust Statistics: Theory and Methods
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S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu · 2012
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Optimal M M -estimation in high-dimensional regression
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High Dimensional Robust M M -Estimation: Asymptotic Variance via Approximate Message Passing
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On robust regression with high-dimensional predictors
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R. Adamczak and P. Wolff · 2014
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Robust estimation of high-dimensional mean regression
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Regularized M M -estimators with nonconvexity: Statistical and algorithmic theory for local optima
P. Loh and M. J. Wainwright · 2014
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Support recovery without incoherence: A case for nonconvex regularization
P. Loh and M. J. Wainwright · 2014
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Influence functions for penalized M M -estimators
A. Medina and A. Marco · 2014
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S. Mendelson · 2014
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V. Öllerer, C. Croux, and A. Alfons · 2014
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