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December 1995 Predicting integrals of random fields using observations on a lattice
Michael L. Stein
Ann. Statist. 23(6): 1975-1990 (December 1995). DOI: 10.1214/aos/1034713643


For a stationary random field Z on $\mathbb{R}^d$, this work studies the asymptotic behavior of predictors of $\int v(x)Z(x)dx$ based on observations on a lattice as the distance between neighbors in the lattice tends to 0. Under a mild condition on the spectral density of Z, an asymptotic expression for the mean-squared error of a predictor of $\int v(x)Z(x)dx$ based on observations on an infinite lattice is derived. For predicting integrals over the unit cube, a simple predictor based just on observations in the unit cube is shown to be asymptotically optimal if v is sufficiently smooth and Z is not too smooth. Modified predictors extend this result to smoother processes.


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Michael L. Stein. "Predicting integrals of random fields using observations on a lattice." Ann. Statist. 23 (6) 1975 - 1990, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0856.62083
MathSciNet: MR1389861
Digital Object Identifier: 10.1214/aos/1034713643

Primary: 62M40
Secondary: 62M20

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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