Canonical correlation analysis for functional data

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Summary

Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation, and is equivalent to solving a generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we propose a new method of constructing canonical correlations and canonical variables for a pair of stochastic processes represented by a finite number of orthonormal basis functions.

References
  • Krzyśko M. (2009): Podstawy wielowymiarowego wnioskowania statysty- cznego [Foundations of multidimensional statistical inference]. Wydawnictwo Naukowe UAM, Poznan.

  • Leurgans S.E., Moyeed R.A., Silverman B.W. (1993): Canonical correlation analy- sis when the data are curves. Journal of the Royal Statistical Society B 55(3): 725{740.

  • Ramsay J.O., Danzell C.J. (1991): Some tools for functional data analysis. Journal of the Royal Statistical Society B 53: 539-572.

  • Ramsay J.O., Silverman B.W. (2005): Functional Data Analysis. Second Edition, Springer.

  • Schott J.R. (2005): Matrix Analysis for Statistics. Second Edition, Wiley, New York.

  • Seber G.A.F. (1984): Multivariate Observations. Wiley, New York.

  • Shmueli G. (2010): To explain or to predict? Statistical Science 25(3): 289{310.

Biometrical Letters

The Journal of Polish Biometric Society

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