Consistent nonparametric regression for functional data under Stone-Besicovitch conditions

Autores
Forzani, Liliana Maria; Fraiman, Jacob Ricardo; Llop Orzan, Pamela Nerina
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we address the problem of nonparametric regression estimation in the infinite-dimensional setting. We start by extending the Stone's seminal result to the case of metric spaces when the probability measure of the explanatory variables is tight. Then, under slight variations on the hypotheses, we state and prove the theorem for general metric measure spaces. From this result, we derive the mean square consistency of the k-NN and kernel estimators if the regression function is bounded and the Besicovitch condition holds. We also prove that, for the uniform kernel estimate, the Besicovitch condition is also necessary in order to attain L1 consistency for almost every x.
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Fraiman, Jacob Ricardo. Universidad de la República. Facultad de Ciencias; Uruguay. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Llop Orzan, Pamela Nerina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Materia
Functional data
Nonparametric regression
Metric spaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/272572

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spelling Consistent nonparametric regression for functional data under Stone-Besicovitch conditionsForzani, Liliana MariaFraiman, Jacob RicardoLlop Orzan, Pamela NerinaFunctional dataNonparametric regressionMetric spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we address the problem of nonparametric regression estimation in the infinite-dimensional setting. We start by extending the Stone's seminal result to the case of metric spaces when the probability measure of the explanatory variables is tight. Then, under slight variations on the hypotheses, we state and prove the theorem for general metric measure spaces. From this result, we derive the mean square consistency of the k-NN and kernel estimators if the regression function is bounded and the Besicovitch condition holds. We also prove that, for the uniform kernel estimate, the Besicovitch condition is also necessary in order to attain L1 consistency for almost every x.Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Fraiman, Jacob Ricardo. Universidad de la República. Facultad de Ciencias; Uruguay. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Llop Orzan, Pamela Nerina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaInstitute of Electrical and Electronics Engineers2012-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/272572Forzani, Liliana Maria; Fraiman, Jacob Ricardo; Llop Orzan, Pamela Nerina; Consistent nonparametric regression for functional data under Stone-Besicovitch conditions; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 58; 11; 11-2012; 6697-67080018-9448CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/6259857/info:eu-repo/semantics/altIdentifier/doi/10.1109/TIT.2012.2209628info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:18:33Zoai:ri.conicet.gov.ar:11336/272572instacron: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:34982025-10-22 11:18:34.143CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
title Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
spellingShingle Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
Forzani, Liliana Maria
Functional data
Nonparametric regression
Metric spaces
title_short Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
title_full Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
title_fullStr Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
title_full_unstemmed Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
title_sort Consistent nonparametric regression for functional data under Stone-Besicovitch conditions
dc.creator.none.fl_str_mv Forzani, Liliana Maria
Fraiman, Jacob Ricardo
Llop Orzan, Pamela Nerina
author Forzani, Liliana Maria
author_facet Forzani, Liliana Maria
Fraiman, Jacob Ricardo
Llop Orzan, Pamela Nerina
author_role author
author2 Fraiman, Jacob Ricardo
Llop Orzan, Pamela Nerina
author2_role author
author
dc.subject.none.fl_str_mv Functional data
Nonparametric regression
Metric spaces
topic Functional data
Nonparametric regression
Metric spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we address the problem of nonparametric regression estimation in the infinite-dimensional setting. We start by extending the Stone's seminal result to the case of metric spaces when the probability measure of the explanatory variables is tight. Then, under slight variations on the hypotheses, we state and prove the theorem for general metric measure spaces. From this result, we derive the mean square consistency of the k-NN and kernel estimators if the regression function is bounded and the Besicovitch condition holds. We also prove that, for the uniform kernel estimate, the Besicovitch condition is also necessary in order to attain L1 consistency for almost every x.
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Fraiman, Jacob Ricardo. Universidad de la República. Facultad de Ciencias; Uruguay. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Llop Orzan, Pamela Nerina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
description In this paper, we address the problem of nonparametric regression estimation in the infinite-dimensional setting. We start by extending the Stone's seminal result to the case of metric spaces when the probability measure of the explanatory variables is tight. Then, under slight variations on the hypotheses, we state and prove the theorem for general metric measure spaces. From this result, we derive the mean square consistency of the k-NN and kernel estimators if the regression function is bounded and the Besicovitch condition holds. We also prove that, for the uniform kernel estimate, the Besicovitch condition is also necessary in order to attain L1 consistency for almost every x.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
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/11336/272572
Forzani, Liliana Maria; Fraiman, Jacob Ricardo; Llop Orzan, Pamela Nerina; Consistent nonparametric regression for functional data under Stone-Besicovitch conditions; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 58; 11; 11-2012; 6697-6708
0018-9448
CONICET Digital
CONICET
url http://hdl.handle.net/11336/272572
identifier_str_mv Forzani, Liliana Maria; Fraiman, Jacob Ricardo; Llop Orzan, Pamela Nerina; Consistent nonparametric regression for functional data under Stone-Besicovitch conditions; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 58; 11; 11-2012; 6697-6708
0018-9448
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/6259857/
info:eu-repo/semantics/altIdentifier/doi/10.1109/TIT.2012.2209628
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
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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