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A simple condition for asymptotic optimality of linear predictions of random fields

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  • Stein, Michael L.

Abstract

Consider linear predictions of a stationary random field at an unobserved location in a bounded region as the observations become increasingly dense in that region. Suppose the ratio of the actual spectral density of the process to the spectral density used to generate the linear predictions tends to a positive finite constant as the frequency increases. Then the sequence of predictions based on the incorrect spectral density and the first n observations are asymptotically optimal as n --> [infinity].

Suggested Citation

  • Stein, Michael L., 1993. "A simple condition for asymptotic optimality of linear predictions of random fields," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 399-404, August.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:5:p:399-404
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    Cited by:

    1. Arafat, Ahmed & Porcu, Emilio & Bevilacqua, Moreno & Mateu, Jorge, 2018. "Equivalence and orthogonality of Gaussian measures on spheres," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 306-318.
    2. Toshihiro Hirano & Yoshihiro Yajima, 2013. "Covariance tapering for prediction of large spatial data sets in transformed random fields," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 913-939, October.
    3. Wenpin Tang & Lu Zhang & Sudipto Banerjee, 2021. "On identifiability and consistency of the nugget in Gaussian spatial process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1044-1070, November.
    4. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.

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