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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 3, Pages 596–608 (Mi tvp274)  

Short Communications

Adjusted Euler–MacLaurin predictor for integrating smooth spatial processes

K. Benhenni, R. Drouilhet

Université Pierre Mendès France - Grenoble 2

Abstract: We consider the problem of predicting integrals of a spatial stationary process $Z$ over a unit square. We construct predictors based on a systematic sampling of size $m^2$ by approximating the existing mean squared derivatives of the process in the two-dimensional Euler–MacLaurin formula by finite differences up to some appropriate order. We show that if the spectral density satisfies $f_{Z}(\omega) =o(|\omega|^{-p})$ for any fixed positive integer $p$, the corresponding mean squared error is of order $m^{-p}$.

Keywords: spatial stationary process, predictor, Euler–MacLaurin formula.

DOI: https://doi.org/10.4213/tvp274

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English version:
Theory of Probability and its Applications, 2004, 48:3, 506–520

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Received: 17.09.1999
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Citation: K. Benhenni, R. Drouilhet, “Adjusted Euler–MacLaurin predictor for integrating smooth spatial processes”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 596–608; Theory Probab. Appl., 48:3 (2004), 506–520

Citation in format AMSBIB
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\paper Adjusted Euler--MacLaurin predictor for
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\jour Teor. Veroyatnost. i Primenen.
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\pages 596--608
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\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 3
\pages 506--520
\crossref{https://doi.org/10.1137/S0040585X97980609}
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