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Penalised robust estimators for sparse and high-dimensional linear models
- Source :
- Statistical methods & applications 30 (2021): 1–48. doi:10.1007/s10260-020-00511-z, info:cnr-pdr/source/autori:Amato U.; Antoniadis A.; De Feis I.; Gijbels I./titolo:Penalised robust estimators for sparse and high-dimensional linear models/doi:10.1007%2Fs10260-020-00511-z/rivista:Statistical methods & applications/anno:2021/pagina_da:1/pagina_a:48/intervallo_pagine:1–48/volume:30, Statistical Methods & Applications
- Publication Year :
- 2021
- Publisher :
- Physica-Verl., [Heidelberg] , Germania, 2021.
-
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 $$p \gg n$$ . 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.
- Subjects :
- Statistics and Probability
Wavelet thresholding
Estimation theory
Computer science
Linear model
Estimator
High-dimensional regression
020206 networking & telecommunications
Feature selection
02 engineering and technology
01 natural sciences
Regularization (mathematics)
010104 statistics & probability
Nonconvex penalties
Contamination
Convergence (routing)
Outlier
0202 electrical engineering, electronic engineering, information engineering
Outliers
0101 mathematics
Statistics, Probability and Uncertainty
Coordinate descent
Algorithm
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Statistical methods & applications 30 (2021): 1–48. doi:10.1007/s10260-020-00511-z, info:cnr-pdr/source/autori:Amato U.; Antoniadis A.; De Feis I.; Gijbels I./titolo:Penalised robust estimators for sparse and high-dimensional linear models/doi:10.1007%2Fs10260-020-00511-z/rivista:Statistical methods & applications/anno:2021/pagina_da:1/pagina_a:48/intervallo_pagine:1–48/volume:30, Statistical Methods & Applications
- Accession number :
- edsair.doi.dedup.....0fd459cc5b7d4eae79376dc7da00e2f4