Principal components for multivariate functional data

Fil: Barrendero, J.R. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.

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Autores principales: Barrendero, J.R., Justel, Ana, Svarc, Marcela
Formato: Documento de Trabajo Documento de trabajo draft
Lenguaje:Inglés
Publicado: Universidad de San Andrés. Departamento de Matemáticas y Ciencias 2012
Acceso en línea:http://hdl.handle.net/10908/635
Aporte de:
Repositorio Digital - Universidad de San Andrés (UdeSa) de Universidad de San Andrés
id I37-R143-10908-635
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spelling I37-R143-10908-6352025-04-23T17:26:49Z Principal components for multivariate functional data Barrendero, J.R. Justel, Ana Svarc, Marcela Fil: Barrendero, J.R. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina. Fil: Justel, Ana. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina. Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina. A principal component method for multivariate functional data is proposed. Data can be arranged in a matrix whose elements are functions so that for each individual a vector of p functions is observed. This set of p curves is reduced to a small number of transformed functions, retaining as much information as possible. The criterion to measure the information loss is the integrated variance. Under mild regular conditions, it is proved that if the original functions are smooth this property is inherited by the principal components. A numerical procedure to obtain the smooth principal components is proposed and the goodness of the dimension reduction is assessed by two new measures of the proportion of explained variability. The method performs as expected in various controlled simulated data sets and provides interesting conclusions when it is applied to real data sets. 2012-07-06T13:19:39Z 2012-07-06T13:19:39Z 2011 Documento de Trabajo info:eu-repo/semantics/workingPaper info:ar-repo/semantics/documento de trabajo info:eu-repo/semantics/draft http://hdl.handle.net/10908/635 eng info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Universidad de San Andrés. Departamento de Matemáticas y Ciencias
institution Universidad de San Andrés
institution_str I-37
repository_str R-143
collection Repositorio Digital - Universidad de San Andrés (UdeSa)
language Inglés
description Fil: Barrendero, J.R. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.
format Documento de Trabajo
Documento de trabajo
Documento de trabajo
draft
author Barrendero, J.R.
Justel, Ana
Svarc, Marcela
spellingShingle Barrendero, J.R.
Justel, Ana
Svarc, Marcela
Principal components for multivariate functional data
author_facet Barrendero, J.R.
Justel, Ana
Svarc, Marcela
author_sort Barrendero, J.R.
title Principal components for multivariate functional data
title_short Principal components for multivariate functional data
title_full Principal components for multivariate functional data
title_fullStr Principal components for multivariate functional data
title_full_unstemmed Principal components for multivariate functional data
title_sort principal components for multivariate functional data
publisher Universidad de San Andrés. Departamento de Matemáticas y Ciencias
publishDate 2012
url http://hdl.handle.net/10908/635
work_keys_str_mv AT barrenderojr principalcomponentsformultivariatefunctionaldata
AT justelana principalcomponentsformultivariatefunctionaldata
AT svarcmarcela principalcomponentsformultivariatefunctionaldata
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