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On the prediction of vector-valued random fields and the spectral distribution of their evanescent component

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  • Cuny, Christophe

Abstract

Let (Xm,n)(m,n)[set membership, variant]Z2 be a Cp-valued wide sense stationary process. We study the prediction theory of such processes according to different total orders on Z2. In the case of a "rational order", we give the spectral distribution of the resulting evanescent component and prove that for two different rational orders, the resulting evanescent components are mutually orthogonal.

Suggested Citation

  • Cuny, Christophe, 2006. "On the prediction of vector-valued random fields and the spectral distribution of their evanescent component," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1842-1869, September.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1842-1869
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    References listed on IDEAS

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    1. Kallianpur, G. & Miamee, A. G. & Niemi, H., 1990. "On the prediction theory of two-parameter stationary random fields," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 120-149, January.
    2. Chiang, Tse-Pei, 1991. "The prediction theory of stationary random fields. III. Fourfold Wold decompositions," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 46-65, April.
    3. Korezlioglu, Hayri & Loubaton, Philippe, 1986. "Spectral factorization of wide sense stationary processes on 2," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 24-47, June.
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