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Biometrika 2000 87(3):587-602; doi:10.1093/biomet/87.3.587
© 2000 by Biometrika Trust
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Principal component models for sparse functional data

GM JamesZ, TJ HastieZZ and CA SugarZ

Z Marshall School of Business, University of Southern California, Los Angeles, CA 90089-0809, USA E-mail: gareth@usc.edu; sugar@usc.edu ZZ Department of Statistics, Stanford University, CA 94305-4065, USA E-mail: hastie@stat.stanford.edu

The elements of a multivariate dataset are often curves rather than single points. Functional principal components can be used to describe the modes of variation of such curves. If one has complete measurements for each individual curve or, as is more common, one has measurements on a fine grid taken at the same time points for all curves, then many standard techniques may be applied. However, curves are often measured at an irregular and sparse set of time points which can differ widely across individuals. We present a technique for handling this more difficult case using a reduced rank mixed effects framework.

Key Words: functional data analysis; growth curve; mixed effects model; principal components; reduced rank estimation


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