Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation

Autores
Forzani, Liliana Maria; Rodriguez, Daniela Andrea; Sued, Raquel Mariela
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well-established paradigm of reduction that keeps all the relevant information in the covariates X that is necessary for the prediction of Y. In practice, SDR has been successfully used as an exploratory tool for modeling after estimation of the sufficient reduction. Nevertheless, even if the estimated reduction is a consistent estimator of the population, there is no theory supporting this step when nonparametric regression is used in the imputed estimator. In this paper, we show that the asymptotic distribution of the nonparametric regression estimator remains unchanged whether the true SDR or its estimator is used. This result allows making inferences, for example, computing confidence intervals for the regression function, thereby avoiding the curse of dimensionality.
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Rodriguez, Daniela Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Fil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Materia
Non-parametric regression
Imputation
Sufficient dimension reduction
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/258298
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimationForzani, Liliana MariaRodriguez, Daniela AndreaSued, Raquel MarielaNon-parametric regressionImputationSufficient dimension reductionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well-established paradigm of reduction that keeps all the relevant information in the covariates X that is necessary for the prediction of Y. In practice, SDR has been successfully used as an exploratory tool for modeling after estimation of the sufficient reduction. Nevertheless, even if the estimated reduction is a consistent estimator of the population, there is no theory supporting this step when nonparametric regression is used in the imputed estimator. In this paper, we show that the asymptotic distribution of the nonparametric regression estimator remains unchanged whether the true SDR or its estimator is used. This result allows making inferences, for example, computing confidence intervals for the regression function, thereby avoiding the curse of dimensionality.Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Rodriguez, Daniela Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaFil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaSpringer2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/258298Forzani, Liliana Maria; Rodriguez, Daniela Andrea; Sued, Raquel Mariela; Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation; Springer; Test; 33; 4; 5-2024; 987-10131133-0686CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s11749-024-00932-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11749-024-00932-yinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2306.10537info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:56:30Zoai:ri.conicet.gov.ar:11336/258298instacron: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 11:56:31.075CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
title Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
spellingShingle Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
Forzani, Liliana Maria
Non-parametric regression
Imputation
Sufficient dimension reduction
title_short Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
title_full Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
title_fullStr Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
title_full_unstemmed Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
title_sort Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation
dc.creator.none.fl_str_mv Forzani, Liliana Maria
Rodriguez, Daniela Andrea
Sued, Raquel Mariela
author Forzani, Liliana Maria
author_facet Forzani, Liliana Maria
Rodriguez, Daniela Andrea
Sued, Raquel Mariela
author_role author
author2 Rodriguez, Daniela Andrea
Sued, Raquel Mariela
author2_role author
author
dc.subject.none.fl_str_mv Non-parametric regression
Imputation
Sufficient dimension reduction
topic Non-parametric regression
Imputation
Sufficient dimension reduction
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well-established paradigm of reduction that keeps all the relevant information in the covariates X that is necessary for the prediction of Y. In practice, SDR has been successfully used as an exploratory tool for modeling after estimation of the sufficient reduction. Nevertheless, even if the estimated reduction is a consistent estimator of the population, there is no theory supporting this step when nonparametric regression is used in the imputed estimator. In this paper, we show that the asymptotic distribution of the nonparametric regression estimator remains unchanged whether the true SDR or its estimator is used. This result allows making inferences, for example, computing confidence intervals for the regression function, thereby avoiding the curse of dimensionality.
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Rodriguez, Daniela Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Fil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
description Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well-established paradigm of reduction that keeps all the relevant information in the covariates X that is necessary for the prediction of Y. In practice, SDR has been successfully used as an exploratory tool for modeling after estimation of the sufficient reduction. Nevertheless, even if the estimated reduction is a consistent estimator of the population, there is no theory supporting this step when nonparametric regression is used in the imputed estimator. In this paper, we show that the asymptotic distribution of the nonparametric regression estimator remains unchanged whether the true SDR or its estimator is used. This result allows making inferences, for example, computing confidence intervals for the regression function, thereby avoiding the curse of dimensionality.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
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/11336/258298
Forzani, Liliana Maria; Rodriguez, Daniela Andrea; Sued, Raquel Mariela; Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation; Springer; Test; 33; 4; 5-2024; 987-1013
1133-0686
CONICET Digital
CONICET
url http://hdl.handle.net/11336/258298
identifier_str_mv Forzani, Liliana Maria; Rodriguez, Daniela Andrea; Sued, Raquel Mariela; Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation; Springer; Test; 33; 4; 5-2024; 987-1013
1133-0686
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://link.springer.com/10.1007/s11749-024-00932-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11749-024-00932-y
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2306.10537
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.229304

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