Marginal integration M-estimators for additive models

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-paramet...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Boente, G., Martínez, A.
Formato:	JOUR
Materias:	Additive models Kernel weights Local M-estimation Marginal integration Robustness
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_11330686_v26_n2_p231_Boente
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_11330686_v26_n2_p231_Boente
record_format	dspace
spelling	todo:paper_11330686_v26_n2_p231_Boente2023-10-03T16:07:56Z Marginal integration M-estimators for additive models Boente, G. Martínez, A. Additive models Kernel weights Local M-estimation Marginal integration Robustness 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. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Martínez, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_11330686_v26_n2_p231_Boente
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Additive models Kernel weights Local M-estimation Marginal integration Robustness
spellingShingle	Additive models Kernel weights Local M-estimation Marginal integration Robustness Boente, G. Martínez, A. Marginal integration M-estimators for additive models
topic_facet	Additive models Kernel weights Local M-estimation Marginal integration Robustness
description	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.
format	JOUR
author	Boente, G. Martínez, A.
author_facet	Boente, G. Martínez, A.
author_sort	Boente, G.
title	Marginal integration M-estimators for additive models
title_short	Marginal integration M-estimators for additive models
title_full	Marginal integration M-estimators for additive models
title_fullStr	Marginal integration M-estimators for additive models
title_full_unstemmed	Marginal integration M-estimators for additive models
title_sort	marginal integration m-estimators for additive models
url	http://hdl.handle.net/20.500.12110/paper_11330686_v26_n2_p231_Boente
work_keys_str_mv	AT boenteg marginalintegrationmestimatorsforadditivemodels AT martineza marginalintegrationmestimatorsforadditivemodels
_version_	1782030995523895296

Marginal integration M-estimators for additive models

Ejemplares similares