When does the screening effect hold?

TL;DR

This paper investigates the conditions under which the screening effect holds in spatial prediction, emphasizing the importance of the spectral density's behavior at high frequencies for the validity of local dependence assumptions.

Contribution

It provides a theoretical framework identifying when an asymptotic screening effect occurs, including proven cases and a conjecture for more general scenarios.

Findings

Screening effect depends on the spectral density's slow variation at high frequencies.

Examples illustrate the complexity of generalizing the screening effect to processes with anisotropic smoothness.

Models with rapid high-frequency spectral changes should be used cautiously.

Abstract

When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the observation locations. This paper explores conditions on the observation locations and the process model under which an asymptotic screening effect holds. A series of examples shows the difficulty in formulating a general result, especially for processes with different degrees of smoothness in different directions, which can naturally occur for spatial-temporal processes. These examples lead to a general conjecture and two special cases of this conjecture are proven. The key condition on the process is that its spectral density should change slowly at high frequencies. Models not satisfying this condition of slow high-frequency change should be used with caution.