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Functional canonical analysis for square integrable stochastic processes. (English) Zbl 1014.62070
Summary: We study the extension of canonical correlations from pairs of random vectors to the case where a data sample consists of pairs of square integrable stochastic processes. Basic questions concerning the definition and existence of functional canonical correlations are addressed and sufficient criteria for the existence of functional canonical correlations are presented. Various properties of functional canonical analysis are discussed. We consider a canonical decomposition, in which the original processes are approximated by means of their canonical components.
MSC:
62H20Statistical measures of associations
62M99Inference from stochastic processes
62G08Nonparametric regression
Software:
fda (R)