Principal components for multivariate functional data
Date
2011
Authors
Barrendero, J.R.
Justel, Ana
Svarc, Marcela
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Journal Title
Journal ISSN
Volume Title
Publisher
Universidad de San Andrés. Departamento de Matemáticas y Ciencias
Abstract
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.
Description
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.
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.