Penalised robust estimators for sparse and high-dimensional linear models

Umberto Amato, Anestis Antoniadis, Italia De Feis () and Irene Gijbels
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Umberto Amato: Italian National Research Council
Anestis Antoniadis: Université Joseph Fourier
Italia De Feis: Italian National Research Council
Irene Gijbels: KU Leuven

Statistical Methods & Applications, 2021, vol. 30, issue 1, No 1, 48 pages

Abstract: Abstract We introduce a new class of robust M-estimators for performing simultaneous parameter estimation and variable selection in high-dimensional regression models. We first explain the motivations for the key ingredient of our procedures which are inspired by regularization methods used in wavelet thresholding in noisy signal processing. The derived penalized estimation procedures are shown to enjoy theoretically the oracle property both in the classical finite dimensional case as well as the high-dimensional case when the number of variables p is not fixed but can grow with the sample size n, and to achieve optimal asymptotic rates of convergence. A fast accelerated proximal gradient algorithm, of coordinate descent type, is proposed and implemented for computing the estimates and appears to be surprisingly efficient in solving the corresponding regularization problems including the case for ultra high-dimensional data where $$p \gg n$$ p ≫ n . Finally, a very extensive simulation study and some real data analysis, compare several recent existing M-estimation procedures with the ones proposed in the paper, and demonstrate their utility and their advantages.

Keywords: Contamination; Outliers; High-dimensional regression; Variable selection; Wavelet thresholding; Nonconvex penalties; Regularization; Primary 62H12; 62G08; Secondary 62G10 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10260-020-00511-z

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