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Abstract:

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.

Registro:

Documento: Artículo
Título:Robust and sparse estimators for linear regression models
Autor:Smucler, E.; Yohai, V.J.
Filiación:Universidad de Buenos Aires - CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires, 1428, Argentina
Palabras clave: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
Año:2017
Volumen:111
Página de inicio:116
Página de fin:130
DOI: http://dx.doi.org/10.1016/j.csda.2017.02.002
Título revista:Computational Statistics and Data Analysis
Título revista abreviado:Comput. Stat. Data Anal.
ISSN:01679473
CODEN:CSDAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v111_n_p116_Smucler

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Citas:

---------- APA ----------
Smucler, E. & Yohai, V.J. (2017) . Robust and sparse estimators for linear regression models. Computational Statistics and Data Analysis, 111, 116-130.
http://dx.doi.org/10.1016/j.csda.2017.02.002
---------- CHICAGO ----------
Smucler, E., Yohai, V.J. "Robust and sparse estimators for linear regression models" . Computational Statistics and Data Analysis 111 (2017) : 116-130.
http://dx.doi.org/10.1016/j.csda.2017.02.002
---------- MLA ----------
Smucler, E., Yohai, V.J. "Robust and sparse estimators for linear regression models" . Computational Statistics and Data Analysis, vol. 111, 2017, pp. 116-130.
http://dx.doi.org/10.1016/j.csda.2017.02.002
---------- VANCOUVER ----------
Smucler, E., Yohai, V.J. Robust and sparse estimators for linear regression models. Comput. Stat. Data Anal. 2017;111:116-130.
http://dx.doi.org/10.1016/j.csda.2017.02.002