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2020 Stein hypothesis and screening effect for covariances with compact support
Emilio Porcu, Viktor Zastavnyi, Moreno Bevilacqua, Xavier Emery
Electron. J. Statist. 14(2): 2510-2528 (2020). DOI: 10.1214/20-EJS1719

Abstract

In spatial statistics, the screening effect historically refers to the situation when the observations located far from the predictand receive a small (ideally, zero) kriging weight. Several factors play a crucial role in this phenomenon: among them, the spatial design, the dimension of the spatial domain where the observations are defined, the mean-square properties of the underlying random field and its covariance function or, equivalently, its spectral density.

The tour de force by Michael L. Stein provides a formal definition of the screening effect and puts emphasis on the Matérn covariance function, advocated as a good covariance function to yield such an effect. Yet, it is often recommended not to use covariance functions with a compact support. This paper shows that some classes of covariance functions being compactly supported allow for a screening effect according to Stein’s definition, in both regular and irregular settings of the spatial design. Further, numerical experiments suggest that the screening effect under a class of compactly supported covariance functions is even stronger than the screening effect under a Matérn model.

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Emilio Porcu. Viktor Zastavnyi. Moreno Bevilacqua. Xavier Emery. "Stein hypothesis and screening effect for covariances with compact support." Electron. J. Statist. 14 (2) 2510 - 2528, 2020. https://doi.org/10.1214/20-EJS1719

Information

Received: 1 November 2019; Published: 2020
First available in Project Euclid: 3 July 2020

zbMATH: 1447.62059
MathSciNet: MR4119265
Digital Object Identifier: 10.1214/20-EJS1719

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