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March, 1988 Asymptotically Efficient Prediction of a Random Field with a Misspecified Covariance Function
Michael L. Stein
Ann. Statist. 16(1): 55-63 (March, 1988). DOI: 10.1214/aos/1176350690

Abstract

Best linear unbiased predictors of a random field can be obtained if the covariance function of the random field is specified correctly. Consider a random field defined on a bounded region $R$. We wish to predict the random field $z(\cdot)$ at a point $x$ in $R$ based on observations $z(x_1), z(x_2), \ldots, z(x_N)$ in $R$, where $\{x_i\}^\infty_{i = 1}$ has $x$ as a limit point but does not contain $x$. Suppose the covariance function is misspecified, but has an equivalent (mutually absolutely continuous) corresponding Gaussian measure to the true covariance function. Then the predictor of $z(x)$ based on $z(x_1), \ldots, z(x_N)$ will be asymptotically efficient as $N$ tends to infinity.

Citation

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Michael L. Stein. "Asymptotically Efficient Prediction of a Random Field with a Misspecified Covariance Function." Ann. Statist. 16 (1) 55 - 63, March, 1988. https://doi.org/10.1214/aos/1176350690

Information

Published: March, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0637.62088
MathSciNet: MR924856
Digital Object Identifier: 10.1214/aos/1176350690

Subjects:
Primary: 62M20
Secondary: 60G30, 60G60

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 1 • March, 1988
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