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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
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
Palabras clave:Additive models; Kernel weights; Local M-estimation; Marginal integration; Robustness
Año:2017
Volumen:26
Número:2
Página de inicio:231
Página de fin:260
DOI: http://dx.doi.org/10.1007/s11749-016-0508-0
Título revista:Test
Título revista abreviado:Test
ISSN:11330686
Registro:http://digital.bl.fcen.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