Robust functional linear regression based on splines

Autores
Maronna, Ricardo A.; Yohai, Victor Jaime
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.
Fil: Maronna, Ricardo A.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Mm Estimate
Natural Splines
Robust Ridge Estimator
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15929
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Robust functional linear regression based on splinesMaronna, Ricardo A.Yohai, Victor JaimeMm EstimateNatural SplinesRobust Ridge Estimatorhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.Fil: Maronna, Ricardo A.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaFil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2013-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15929Maronna, Ricardo A.; Yohai, Victor Jaime; Robust functional linear regression based on splines; Elsevier Science; Computational Statistics And Data Analysis; 65; 9-2013; 46-550167-9473enginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.csda.2011.11.014info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0167947311004117info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:59:19Zoai:ri.conicet.gov.ar:11336/15929instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:59:20.101CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Robust functional linear regression based on splines
title Robust functional linear regression based on splines
spellingShingle Robust functional linear regression based on splines
Maronna, Ricardo A.
Mm Estimate
Natural Splines
Robust Ridge Estimator
title_short Robust functional linear regression based on splines
title_full Robust functional linear regression based on splines
title_fullStr Robust functional linear regression based on splines
title_full_unstemmed Robust functional linear regression based on splines
title_sort Robust functional linear regression based on splines
dc.creator.none.fl_str_mv Maronna, Ricardo A.
Yohai, Victor Jaime
author Maronna, Ricardo A.
author_facet Maronna, Ricardo A.
Yohai, Victor Jaime
author_role author
author2 Yohai, Victor Jaime
author2_role author
dc.subject.none.fl_str_mv Mm Estimate
Natural Splines
Robust Ridge Estimator
topic Mm Estimate
Natural Splines
Robust Ridge Estimator
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.
Fil: Maronna, Ricardo A.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.
publishDate 2013
dc.date.none.fl_str_mv 2013-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/15929
Maronna, Ricardo A.; Yohai, Victor Jaime; Robust functional linear regression based on splines; Elsevier Science; Computational Statistics And Data Analysis; 65; 9-2013; 46-55
0167-9473
url http://hdl.handle.net/11336/15929
identifier_str_mv Maronna, Ricardo A.; Yohai, Victor Jaime; Robust functional linear regression based on splines; Elsevier Science; Computational Statistics And Data Analysis; 65; 9-2013; 46-55
0167-9473
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.csda.2011.11.014
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0167947311004117
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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