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August, 1993 Asymptotic Properties of Centered Systematic Sampling for Predicting Integrals of Spatial Processes
Michael L. Stein
Ann. Appl. Probab. 3(3): 874-880 (August, 1993). DOI: 10.1214/aoap/1177005369

Abstract

This paper studies the asymptotic mean squared error for predicting the integral of a weakly stationary spatial process over a unit cube based on a centered systematic sample. For processes whose spectral density decays sufficiently slowly at infinity, the asymptotic mean squared error takes a form similar to that obtained by letting the cube increase in size with the number of observations. However, if the spectral density decays faster than a certain critical rate, then the asymptotic mean squared error takes on a completely different form. By adjusting the weights given to observations near an edge of the cube, it is possible to obtain asymptotic results for the fixed cube that again resemble those for the increasing cube.

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Michael L. Stein. "Asymptotic Properties of Centered Systematic Sampling for Predicting Integrals of Spatial Processes." Ann. Appl. Probab. 3 (3) 874 - 880, August, 1993. https://doi.org/10.1214/aoap/1177005369

Information

Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0779.62091
MathSciNet: MR1233631
Digital Object Identifier: 10.1214/aoap/1177005369

Subjects:
Primary: 62M40
Secondary: 62M20

Keywords: fixed-domain asymptotics , increasing-domain asymptotics , numerical integration , spatial statistics

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 3 • August, 1993
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