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Tensor product splines and functional principal components. (English) Zbl 1435.62451
Summary: Functional principal component analysis for sparse longitudinal data usually proceeds by first smoothing the covariance surface, and then obtaining an eigendecomposition of the associated covariance operator. Here we consider the use of penalized tensor product splines for the initial smoothing step. Drawing on a result regarding finite-rank symmetric integral operators, we derive an explicit spline representation of the estimated eigenfunctions, and show that the effect of penalization can be notably disparate for alternative approaches to tensor product smoothing. The latter phenomenon is illustrated with two data sets derived from magnetic resonance imaging of the human brain.
Reviewer: Reviewer (Berlin)
62R10 Functional data analysis
62H25 Factor analysis and principal components; correspondence analysis
65D07 Numerical computation using splines
47A80 Tensor products of linear operators
62H35 Image analysis in multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
60L90 Applications of rough analysis
fda (R); gamair; R; refund; SemiPar
Full Text: DOI
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