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

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 dis...

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Detalles Bibliográficos
Autor principal:	Boente, Graciela Lina
Publicado:	2014
Materias:	Elliptical distributions Functional data analysis Principal components
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v131_n_p254_Boente http://hdl.handle.net/20.500.12110/paper_0047259X_v131_n_p254_Boente
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0047259X_v131_n_p254_Boente
record_format	dspace
spelling	paper:paper_0047259X_v131_n_p254_Boente2023-06-08T15:05:35Z A characterization of elliptical distributions and some optimality properties of principal components for functional data Boente, Graciela Lina Elliptical distributions Functional data analysis Principal components 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. © 2014 Elsevier Inc. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v131_n_p254_Boente http://hdl.handle.net/20.500.12110/paper_0047259X_v131_n_p254_Boente
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Elliptical distributions Functional data analysis Principal components
spellingShingle	Elliptical distributions Functional data analysis Principal components Boente, Graciela Lina A characterization of elliptical distributions and some optimality properties of principal components for functional data
topic_facet	Elliptical distributions Functional data analysis Principal components
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. © 2014 Elsevier Inc.
author	Boente, Graciela Lina
author_facet	Boente, Graciela Lina
author_sort	Boente, Graciela Lina
title	A characterization of elliptical distributions and some optimality properties of principal components for functional data
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	characterization of elliptical distributions and some optimality properties of principal components for functional data
publishDate	2014
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v131_n_p254_Boente http://hdl.handle.net/20.500.12110/paper_0047259X_v131_n_p254_Boente
work_keys_str_mv	AT boentegracielalina acharacterizationofellipticaldistributionsandsomeoptimalitypropertiesofprincipalcomponentsforfunctionaldata AT boentegracielalina characterizationofellipticaldistributionsandsomeoptimalitypropertiesofprincipalcomponentsforfunctionaldata
_version_	1768544949601566720

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

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