Abstract:
Additive regression models have a long history in multivariate non-parametric regression. They provide a model in which the regression function is decomposed as a sum of functions, each of them depending only on a single explanatory variable. The advantage of additive models over general non-parametric regression models is that they allow to obtain estimators converging at the optimal univariate rate avoiding the so-called curse of dimensionality. Beyond backfitting, marginal integration is a common procedure to estimate each component in additive models. In this paper, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated with the marginal integration procedure. The proposed estimators are consistent and asymptotically normally distributed. A simulation study allows to show the advantage of the proposal over the classical one when outliers are present in the responses, leading to estimators with good robustness and efficiency properties. © 2016, Sociedad de Estadística e Investigación Operativa.
Registro:
Documento: |
Artículo
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Título: | Marginal integration M-estimators for additive models |
Autor: | Boente, G.; Martínez, A. |
Filiación: | Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
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Palabras clave: | Additive models; Kernel weights; Local M-estimation; Marginal integration; Robustness |
Año: | 2017
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Volumen: | 26
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Número: | 2
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Página de inicio: | 231
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Página de fin: | 260
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DOI: |
http://dx.doi.org/10.1007/s11749-016-0508-0 |
Título revista: | Test
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Título revista abreviado: | Test
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ISSN: | 11330686
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v26_n2_p231_Boente |
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Citas:
---------- APA ----------
Boente, G. & Martínez, A.
(2017)
. Marginal integration M-estimators for additive models. Test, 26(2), 231-260.
http://dx.doi.org/10.1007/s11749-016-0508-0---------- CHICAGO ----------
Boente, G., Martínez, A.
"Marginal integration M-estimators for additive models"
. Test 26, no. 2
(2017) : 231-260.
http://dx.doi.org/10.1007/s11749-016-0508-0---------- MLA ----------
Boente, G., Martínez, A.
"Marginal integration M-estimators for additive models"
. Test, vol. 26, no. 2, 2017, pp. 231-260.
http://dx.doi.org/10.1007/s11749-016-0508-0---------- VANCOUVER ----------
Boente, G., Martínez, A. Marginal integration M-estimators for additive models. Test. 2017;26(2):231-260.
http://dx.doi.org/10.1007/s11749-016-0508-0