Functional canonical analysis for square integrable stochastic processes |
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| Authors: | Guozhong HeHans-Georg Müller Jane-Ling Wang |
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| Institution: | a The California Diabetes Control Program, University of California, San Francisco/DHS, 601 North 7th Street, MS 675, Sacramento, CA 94234, USA
b Department of Statistics, University of California, One Shields Avenue, Davis, CA 95616, USA |
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| Abstract: | We study the extension of canonical correlation 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 correlation are addressed and sufficient criteria for the existence of functional canonical correlation 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. |
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| Keywords: | primary 62H20 secondary 62G08 60G12 |
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