Stein hypothesis and screening effect for covariances with compact support
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2020Metadata
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Porcu, Emilio
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Stein hypothesis and screening effect for covariances with compact support
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In spatial statistics, the screening effect historically refers to the situation when the observations located far from the predict and 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 Matern 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 Matern model.
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Electronic Journal of Statistics (2020) 14:2
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