Principal components for multivariate functional data

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dc.creator.AutorBarrendero, J.R.
dc.creator.AutorJustel, Ana
dc.creator.AutorSvarc, Marcela
dc.date.accessioned2012-07-06T13:19:39Z
dc.date.available2012-07-06T13:19:39Z
dc.date.issued2011
dc.descriptionFil: Barrendero, J.R. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.
dc.descriptionFil: Justel, Ana. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.
dc.descriptionFil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.
dc.description.abstractA 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.
dc.formatapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10908/635
dc.languageeng
dc.publisherUniversidad de San Andrés. Departamento de Matemáticas y Ciencias
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightshttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titlePrincipal components for multivariate functional data
dc.typeDocumento de Trabajo
dc.typeinfo:eu-repo/semantics/workingPaper
dc.typeinfo:ar-repo/semantics/documento de trabajo
dc.typeinfo:eu-repo/semantics/draft
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