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On the prediction theory of two-parameter stationary random fields

Author

Listed:
  • Kallianpur, G.
  • Miamee, A. G.
  • Niemi, H.

Abstract

The paper develops the spectral theory corresponding to the various time domain Wold decompositions of a discrete two-parameter stationary second-order random field (ssorf). Appropriate Szegö-type error formulas are established. Minimality and interpolability are defined for ssorf's and sufficient spectral criteria for these are derived. Partial results are also obtained which help to determine, via spectral methods, some of the multiplicities introduced by Kallianpur and Mandrekar in their time domain analysis of ssorf's.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:32:y:1990:i:1:p:120-149
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    Citations

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    Cited by:

    1. 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.
    2. Hurd, H. & Kallianpur, G. & Farshidi, J., 2004. "Correlation and spectral theory for periodically correlated random fields indexed on Z2," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 359-383, August.
    3. Kliger, Mark & Francos, Joseph M., 2010. "The rank of the covariance matrix of an evanescent field," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 692-705, March.
    4. Kliger, Mark & Francos, Joseph M., 2007. "Asymptotic normality of the sample mean and covariances of evanescent fields in noise," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1853-1875, November.
    5. Kohli, P. & Pourahmadi, M., 2014. "Some prediction problems for stationary random fields with quarter-plane past," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 112-125.

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