Robust and sparse estimators for linear regression models

Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust...

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Detalles Bibliográficos
Publicado: 2017
Materias:
Lasso
MM-estimators
Oracle property
Robust regression
Sparse linear models
Computational methods
Data handling
Asymptotic distributions
Asymptotic properties
High-dimensional models
Linear regression models
Oracle properties
Robust regressions
Regression analysis
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v111_n_p116_Smucler
http://hdl.handle.net/20.500.12110/paper_01679473_v111_n_p116_Smucler
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01679473_v111_n_p116_Smucler
record_format dspace
spelling paper:paper_01679473_v111_n_p116_Smucler2023-06-08T15:17:07Z Robust and sparse estimators for linear regression models Lasso MM-estimators Oracle property Robust regression Sparse linear models Computational methods Data handling Asymptotic distributions Asymptotic properties High-dimensional models Lasso Linear regression models MM-estimators Oracle properties Robust regressions Regression analysis Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ 1 -penalized MM-estimators and MM-estimators with an adaptive ℓ 1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ 1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A). © 2017 Elsevier B.V. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v111_n_p116_Smucler http://hdl.handle.net/20.500.12110/paper_01679473_v111_n_p116_Smucler
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Lasso
MM-estimators
Oracle property
Robust regression
Sparse linear models
Computational methods
Data handling
Asymptotic distributions
Asymptotic properties
High-dimensional models
Lasso
Linear regression models
MM-estimators
Oracle properties
Robust regressions
Regression analysis
spellingShingle Lasso
MM-estimators
Oracle property
Robust regression
Sparse linear models
Computational methods
Data handling
Asymptotic distributions
Asymptotic properties
High-dimensional models
Lasso
Linear regression models
MM-estimators
Oracle properties
Robust regressions
Regression analysis
Robust and sparse estimators for linear regression models
topic_facet Lasso
MM-estimators
Oracle property
Robust regression
Sparse linear models
Computational methods
Data handling
Asymptotic distributions
Asymptotic properties
High-dimensional models
Lasso
Linear regression models
MM-estimators
Oracle properties
Robust regressions
Regression analysis
description Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ 1 -penalized MM-estimators and MM-estimators with an adaptive ℓ 1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ 1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A). © 2017 Elsevier B.V.
title Robust and sparse estimators for linear regression models
title_short Robust and sparse estimators for linear regression models
title_full Robust and sparse estimators for linear regression models
title_fullStr Robust and sparse estimators for linear regression models
title_full_unstemmed Robust and sparse estimators for linear regression models
title_sort robust and sparse estimators for linear regression models
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v111_n_p116_Smucler
http://hdl.handle.net/20.500.12110/paper_01679473_v111_n_p116_Smucler
_version_ 1768543941119967232

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