A characterization of elliptical distributions and some optimality properties of principal components for functional data

Autores
Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; Tyler, David E.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical distributions on separable Hilbert spaces, namely we show that the class of elliptical distributions in the infinite-dimensional case is equivalent to the class of scale mixtures of Gaussian distributions on the space. Using this characterization, we establish a stochastic optimality property for the principal component subspaces associated with an elliptically distributed random element, which holds even when second moments do not exist. In addition, when second moments exist, we establish an optimality property regarding unitarily invariant norms of the residuals covariance operator.
Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Salibian Barrera, Matías Octavio. University Of British Columbia; Canadá
Fil: Tyler, David E.. Rutgers University; Estados Unidos
Materia
Elliptical Distributions
Functional Data Analysis
Principal Components
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18730
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A characterization of elliptical distributions and some optimality properties of principal components for functional dataBoente Boente, Graciela LinaSalibian Barrera, Matías OctavioTyler, David E.Elliptical DistributionsFunctional Data AnalysisPrincipal Componentshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical distributions on separable Hilbert spaces, namely we show that the class of elliptical distributions in the infinite-dimensional case is equivalent to the class of scale mixtures of Gaussian distributions on the space. Using this characterization, we establish a stochastic optimality property for the principal component subspaces associated with an elliptically distributed random element, which holds even when second moments do not exist. In addition, when second moments exist, we establish an optimality property regarding unitarily invariant norms of the residuals covariance operator.Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Salibian Barrera, Matías Octavio. University Of British Columbia; CanadáFil: Tyler, David E.. Rutgers University; Estados UnidosElsevier Inc2014-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18730Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; Tyler, David E.; A characterization of elliptical distributions and some optimality properties of principal components for functional data; Elsevier Inc; Journal Of Multivariate Analysis; 131; 10-2014; 254-2640047-259XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmva.2014.07.006info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0047259X14001638info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:40Zoai:ri.conicet.gov.ar:11336/18730instacron: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 09:33:41.188CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A characterization of elliptical distributions and some optimality properties of principal components for functional data
title A characterization of elliptical distributions and some optimality properties of principal components for functional data
spellingShingle A characterization of elliptical distributions and some optimality properties of principal components for functional data
Boente Boente, Graciela Lina
Elliptical Distributions
Functional Data Analysis
Principal Components
title_short A characterization of elliptical distributions and some optimality properties of principal components for functional data
title_full A characterization of elliptical distributions and some optimality properties of principal components for functional data
title_fullStr A characterization of elliptical distributions and some optimality properties of principal components for functional data
title_full_unstemmed A characterization of elliptical distributions and some optimality properties of principal components for functional data
title_sort A characterization of elliptical distributions and some optimality properties of principal components for functional data
dc.creator.none.fl_str_mv Boente Boente, Graciela Lina
Salibian Barrera, Matías Octavio
Tyler, David E.
author Boente Boente, Graciela Lina
author_facet Boente Boente, Graciela Lina
Salibian Barrera, Matías Octavio
Tyler, David E.
author_role author
author2 Salibian Barrera, Matías Octavio
Tyler, David E.
author2_role author
author
dc.subject.none.fl_str_mv Elliptical Distributions
Functional Data Analysis
Principal Components
topic Elliptical Distributions
Functional Data Analysis
Principal Components
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical distributions on separable Hilbert spaces, namely we show that the class of elliptical distributions in the infinite-dimensional case is equivalent to the class of scale mixtures of Gaussian distributions on the space. Using this characterization, we establish a stochastic optimality property for the principal component subspaces associated with an elliptically distributed random element, which holds even when second moments do not exist. In addition, when second moments exist, we establish an optimality property regarding unitarily invariant norms of the residuals covariance operator.
Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Salibian Barrera, Matías Octavio. University Of British Columbia; Canadá
Fil: Tyler, David E.. Rutgers University; Estados Unidos
description As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical distributions on separable Hilbert spaces, namely we show that the class of elliptical distributions in the infinite-dimensional case is equivalent to the class of scale mixtures of Gaussian distributions on the space. Using this characterization, we establish a stochastic optimality property for the principal component subspaces associated with an elliptically distributed random element, which holds even when second moments do not exist. In addition, when second moments exist, we establish an optimality property regarding unitarily invariant norms of the residuals covariance operator.
publishDate 2014
dc.date.none.fl_str_mv 2014-10
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/11336/18730
Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; Tyler, David E.; A characterization of elliptical distributions and some optimality properties of principal components for functional data; Elsevier Inc; Journal Of Multivariate Analysis; 131; 10-2014; 254-264
0047-259X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18730
identifier_str_mv Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; Tyler, David E.; A characterization of elliptical distributions and some optimality properties of principal components for functional data; Elsevier Inc; Journal Of Multivariate Analysis; 131; 10-2014; 254-264
0047-259X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmva.2014.07.006
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0047259X14001638
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
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 13.070432

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