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Principal Component Analysis for a Stationary Random Function Defined on a Locally Compact Abelian Group

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  • Boudou, A.
  • Dauxois, J.

Abstract

When Z is a random L2H-valued measure, where H is a Hilbert space, we prove that there exists an L2q-valued measure, which may depend on constraints and which best sums up the random measure Z according to a stationary criterion. Then a technique to reduce a random function is deduced from the above result. The random function is defined on a locally compact abelian group and is stationary and continuous. This work generalizes Brillinger's results on stationary time series.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:51:y:1994:i:1:p:1-16
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    Cited by:

    1. Boudou, Alain & Viguier-Pla, Sylvie, 2022. "Principal components analysis and cyclostationarity," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    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. 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.
    4. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Boudou, Alain & Romain, Yves, 2010. "On the integral with respect to the tensor product of two random measures," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 385-394, February.
    6. Boudou, Alain, 2006. "Approximation of the principal components analysis of a stationary function," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 571-578, March.
    7. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    8. Ombao, Hernando & Ringo Ho, Moon-ho, 2006. "Time-dependent frequency domain principal components analysis of multichannel non-stationary signals," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2339-2360, May.

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