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Centered and non-centered principal component analyses in the frequency domain

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  • Boudou, A.
  • Cabral, E.N.
  • Romain, Y.

Abstract

Given a stationary multidimensional process and the process which is deduced after centering, we wish to study possible links between the principal component analyses, in the frequency domain, of these two processes. It is well known that there is, a priori, no obvious relationship between the centered and non-centered principal component analyses in the temporal domain. Furthermore, we also know that principal component analysis in the frequency domain is reduced to principal component analysis of each spectral component. In this paper, we show the remarkable result that the centered and non-centered principal component analyses in the frequency domain are equal except for a given frequency.

Suggested Citation

  • Boudou, A. & Cabral, E.N. & Romain, Y., 2010. "Centered and non-centered principal component analyses in the frequency domain," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 96-103, January.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:2:p:96-103
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    References listed on IDEAS

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    1. Boudou, A. & Dauxois, J., 1994. "Principal Component Analysis for a Stationary Random Function Defined on a Locally Compact Abelian Group," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 1-16, October.
    2. Boudou, Alain & Romain, Yves, 2002. "On spectral and random measures associated to discrete and continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 145-157, September.
    3. Rosenberg, Milton, 1974. "Operators as spectral integrals of operator-valued functions from the study of multivariate stationary stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 4(2), pages 166-209, June.
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    Cited by:

    1. Heewon Park & Sadanori Konishi, 2020. "Sparse common component analysis for multiple high-dimensional datasets via noncentered principal component analysis," Statistical Papers, Springer, vol. 61(6), pages 2283-2311, December.

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