Stein hypothesis and screening effect for covariances with compact support

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.