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Abstract:
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A general framework is developed for the analysis of functional data that derives from the Loeve/Parzen isometry between the Hilbert space spanned by a second order process and the reproducing kernel Hilbert space (RKHS) generated by its covariance kernel. Using this RKHS framework, population foundations are laid for statistical techniques such as functional analysis of variance, functional canonical correlation, functional discriminant analysis, functional factor analysis and functional regression. Computational methods that have been implemented for data analysis applications are described along with some supporting large sample theory.
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