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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/272572
Ver los metadatos del registro completo
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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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.229304 |