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February 2002 The screening effect in Kriging
Michael L. Stein
Ann. Statist. 30(1): 298-323 (February 2002). DOI: 10.1214/aos/1015362194


When predicting the value of a stationary random field at a location x in some region in which one has a large number of observations, it may be difficult to compute the optimal predictor. One simple way to reduce the computational burden is to base the predictor only on those observations nearest to x. As long as the number of observations used in the predictor is sufficiently large, one might generally expect the best predictor based on these observations to be nearly optimal relative to the best predictor using all observations. Indeed, this phenomenon has been empirically observed in numerous circumstances and is known as the screening effect in the geostatistical literature. For linear predictors, when observations are on a regular grid, this work proves that there generally is a screening effect as the grid becomes increasingly dense. This result requires that, at high frequencies, the spectral density of the random field not decay faster than algebraically and not vary too quickly. Examples demonstrate that there may be no screening effect if these conditions on the spectral density are violated.


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Michael L. Stein. "The screening effect in Kriging." Ann. Statist. 30 (1) 298 - 323, February 2002.


Published: February 2002
First available in Project Euclid: 5 March 2002

zbMATH: 1012.62102
MathSciNet: MR1892665
Digital Object Identifier: 10.1214/aos/1015362194

Primary: 62M20
Secondary: 60G25 , 62M40

Keywords: asymptotics , best linear prediction , Random field , regular variation , self-affine , Self-similar

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.30 • No. 1 • February 2002
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