An Introduction to Theoretical Properties of Functional Principal Component Analysis
by Ngoc M. Tran
Abstract: The term functional data refers to data where each observation is a
curve, a surface, or a hypersurface, as opposed to a point or a finite-dimensional vector.
Functional data are intrinsically infinite dimensional and measurements on the same
curve display high correlation, making assumptions of classical multivariate models
invalid. An alternative approach, functional principal components analysis (FPCA),
is used in this area as an important data analysis tool. The purpose of this talk is to
provide a summary of some theoretical properties of FPCA when used in functional data
exploratory analysis and functional linear regression. Practical issues in implementing
FPCA and further topics in functional data analysis are also discussed, however, the
emphasis is given to asymptotic and consistency results, their proofs and implications.
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