Nonparametric estimation of a surrogate density function in infinite-dimensional spaces

Autores
Ferraty, Frédéric; Kudraszow, Nadia Laura; Vieu, Philippe
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate.
Fil: Ferraty, Frédéric. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; Francia
Fil: Kudraszow, Nadia Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Vieu, Philippe. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; Francia
Materia
Functional Data
K-Nearest Neighbour Method
Kernel Estimators
Small Ball Probability
Smoother Bootstrap
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:11336/79667
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/79667
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nonparametric estimation of a surrogate density function in infinite-dimensional spacesFerraty, FrédéricKudraszow, Nadia LauraVieu, PhilippeFunctional DataK-Nearest Neighbour MethodKernel EstimatorsSmall Ball ProbabilitySmoother Bootstraphttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate.Fil: Ferraty, Frédéric. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; FranciaFil: Kudraszow, Nadia Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Vieu, Philippe. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; FranciaTaylor & Francis Ltd2012-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/79667Ferraty, Frédéric; Kudraszow, Nadia Laura; Vieu, Philippe; Nonparametric estimation of a surrogate density function in infinite-dimensional spaces; Taylor & Francis Ltd; Journal Of Nonparametric Statistics; 24; 2; 6-2012; 447-4641048-52521029-0311CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1080/10485252.2012.671943info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/10485252.2012.671943info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:15:59Zoai:ri.conicet.gov.ar:11336/79667instacron: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 10:15:59.823CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
title Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
spellingShingle Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
Ferraty, Frédéric
Functional Data
K-Nearest Neighbour Method
Kernel Estimators
Small Ball Probability
Smoother Bootstrap
title_short Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
title_full Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
title_fullStr Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
title_full_unstemmed Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
title_sort Nonparametric estimation of a surrogate density function in infinite-dimensional spaces
dc.creator.none.fl_str_mv Ferraty, Frédéric
Kudraszow, Nadia Laura
Vieu, Philippe
author Ferraty, Frédéric
author_facet Ferraty, Frédéric
Kudraszow, Nadia Laura
Vieu, Philippe
author_role author
author2 Kudraszow, Nadia Laura
Vieu, Philippe
author2_role author
author
dc.subject.none.fl_str_mv Functional Data
K-Nearest Neighbour Method
Kernel Estimators
Small Ball Probability
Smoother Bootstrap
topic Functional Data
K-Nearest Neighbour Method
Kernel Estimators
Small Ball Probability
Smoother Bootstrap
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate.
Fil: Ferraty, Frédéric. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; Francia
Fil: Kudraszow, Nadia Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Vieu, Philippe. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; Francia
description A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate.
publishDate 2012
dc.date.none.fl_str_mv 2012-06
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/11336/79667
Ferraty, Frédéric; Kudraszow, Nadia Laura; Vieu, Philippe; Nonparametric estimation of a surrogate density function in infinite-dimensional spaces; Taylor & Francis Ltd; Journal Of Nonparametric Statistics; 24; 2; 6-2012; 447-464
1048-5252
1029-0311
CONICET Digital
CONICET
url http://hdl.handle.net/11336/79667
identifier_str_mv Ferraty, Frédéric; Kudraszow, Nadia Laura; Vieu, Philippe; Nonparametric estimation of a surrogate density function in infinite-dimensional spaces; Taylor & Francis Ltd; Journal Of Nonparametric Statistics; 24; 2; 6-2012; 447-464
1048-5252
1029-0311
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1080/10485252.2012.671943
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/10485252.2012.671943
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
dc.publisher.none.fl_str_mv Taylor & Francis Ltd
publisher.none.fl_str_mv Taylor & Francis Ltd
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_ 1844614100445822976
score 13.070432

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