Abstract:
In this paper, we propose a new family of robust regression estimators, which we call bounded residual scale estimators (BRS-estimators) which are simultaneously highly robust and highly efficient for small samples with normally distributed errors. To define these estimators it is required to have a robust M-scale and a family of robust MM-estimators. We start by choosing in this family a highly robust initial estimator but not necessarily highly efficient. Loosely speaking, the BRS-estimator is defined as the estimator in the MM family which is closest to the LSE among those with a robust M-scale sufficiently close to the one of the initial estimators. The efficiency of the BRS is derived from the fact that when there are not outliers in the sample and the errors are normally distributed, the scale of the LSE is similar to the one of the initial estimator. The robustness of the BRS-estimator comes from the fact that its robust scale is close to the one of the initial highly robust estimator. The results of a Monte Carlo study show that the proposed estimator has a high finite-sample efficiency, and is highly resistant to outlier contamination. © Springer International Publishing Switzerland 2015.
Registro:
| Documento: |
Parte de libro
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| Título: | Highly robust and highly finite sample efficient estimators for the linear model |
| Autor: | Smucler, E.; Yohai, V.J. |
| Filiación: | Instituto de Calculo, Universidad de Buenos Aires, Departamento de Matematicas and Instituto de Calculo, Intendente Gairaldes 2160, Buenos Aires, 1428, Argentina
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| Palabras clave: | Brakdown point; Finite sample efficiency; MM-estimators; Efficiency; Normal distribution; Sampling; Statistics; Brakdown point; Efficient estimator; Finite samples; Initial estimators; Linear modeling; MM-estimators; Robust estimators; Robust regressions; Estimation |
| Año: | 2015
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| Página de inicio: | 91
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| Página de fin: | 108
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| DOI: |
http://dx.doi.org/10.1007/978-3-319-22404-6_6 |
| Título revista: | Modern Nonparametric, Robust and Multivariate Methods: Festschrift in Honour of Hannu Oja
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| Título revista abreviado: | Modern Nonparametric, Robust and Multivar. Methods: Festschrift in Honour of Hannu Oja
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97833192_v_n_p91_Smucler |
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Citas:
---------- APA ----------
Smucler, E. & Yohai, V.J.
(2015)
. Highly robust and highly finite sample efficient estimators for the linear model. Modern Nonparametric, Robust and Multivariate Methods: Festschrift in Honour of Hannu Oja, 91-108.
http://dx.doi.org/10.1007/978-3-319-22404-6_6---------- CHICAGO ----------
Smucler, E., Yohai, V.J.
"Highly robust and highly finite sample efficient estimators for the linear model"
. Modern Nonparametric, Robust and Multivariate Methods: Festschrift in Honour of Hannu Oja
(2015) : 91-108.
http://dx.doi.org/10.1007/978-3-319-22404-6_6---------- MLA ----------
Smucler, E., Yohai, V.J.
"Highly robust and highly finite sample efficient estimators for the linear model"
. Modern Nonparametric, Robust and Multivariate Methods: Festschrift in Honour of Hannu Oja, 2015, pp. 91-108.
http://dx.doi.org/10.1007/978-3-319-22404-6_6---------- VANCOUVER ----------
Smucler, E., Yohai, V.J. Highly robust and highly finite sample efficient estimators for the linear model. Modern Nonparametric, Robust and Multivar. Methods: Festschrift in Honour of Hannu Oja. 2015:91-108.
http://dx.doi.org/10.1007/978-3-319-22404-6_6