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Functional canonical analysis for square integrable stochastic processes

Author

Listed:
  • He, Guozhong
  • Müller, Hans-Georg
  • Wang, Jane-Ling

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.

Suggested Citation

  • He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
  • Handle: RePEc:eee:jmvana:v:85:y:2003:i:1:p:54-77
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    Cited by:

    1. Cho, Haeran & Goude, Yannig & Brossat, Xavier & Yao, Qiwei, 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.
    2. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Rejoinder on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 52-58, March.
    3. repec:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-015-9478-5 is not listed on IDEAS
    4. 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.
    5. 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;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    6. Peter Hall & You-Jun Yang, 2010. "Ordering and selecting components in multivariate or functional data linear prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 93-110.
    7. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
    8. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    9. Shen, Cencheng & Sun, Ming & Tang, Minh & Priebe, Carey E., 2014. "Generalized canonical correlation analysis for classification," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 310-322.
    10. Ross Iaci & T.N. Sriram & Xiangrong Yin, 2010. "Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis," Biometrics, The International Biometric Society, vol. 66(4), pages 1107-1118, December.
    11. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    12. repec:bla:scjsta:v:44:y:2017:i:1:p:1-20 is not listed on IDEAS
    13. Mariano J. Valderrama & Francisco A. Ocaña & Ana M. Aguilera & Francisco M. Ocaña-Peinado, 2010. "Forecasting Pollen Concentration by a Two-Step Functional Model," Biometrics, The International Biometric Society, vol. 66(2), pages 578-585, June.
    14. Fan, Zengyan & Lian, Heng, 2016. "Minimax convergence rates for kernel CCA," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 183-190.

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