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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/258298
Ver los metadatos del registro completo
id |
CONICETDig_d9cac68878b8df49fc73b6fa53fdcc97 |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/258298 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
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 |
_version_ |
1846782272370376704 |
score |
13.229304 |