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Functional canonical analysis for square integrable stochastic processes

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  • He, Guozhong
  • Müller, Hans-Georg
  • Wang, Jane-Ling
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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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 85 (2003)
    Issue (Month): 1 (April)
    Pages: 54-77

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    Handle: RePEc:eee:jmvana:v:85:y:2003:i:1:p:54-77

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    Related research

    Keywords: Canonical correlation Canonical decomposition Covariance operator Functional data analysis Hilbert-Schmidt operator Inverse problem;

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    Cited by:
    1. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(1), pages 1-29, May.
    2. A. Onatski & V. Karguine, 2005. "Curve Forecasting by Functional Autoregression," Computing in Economics and Finance 2005 59, Society for Computational Economics.
    3. Harezlak, Jaroslaw & Coull, Brent A. & Laird, Nan M. & Magari, Shannon R. & Christiani, David C., 2007. "Penalized solutions to functional regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4911-4925, June.
    4. Haeran Cho & Yannig Goude & Xavier Brossat & Qiwei Yao, 2013. "Modeling and forecasting daily electricity load curves: a hybrid approach," LSE Research Online Documents on Economics 49634, London School of Economics and Political Science, LSE Library.

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