Testing for Simplification in Spatial Models

TL;DR: Methods for testing models for the spatial process often make simplifying assumptions, including axial symmetry and separability are considered and tests based on sample covariances, testsbased on the sample spectrum, and model-based tests are compared.

Abstract: Data collected on a rectangular lattice occur frequently in many areas such as field trials, geostatistics, remotely sensed data, and image analysis. Models for the spatial process often make simplifying assumptions, including axial symmetry and separability. We consider methods for testing these assumptions and compare tests based on sample covariances, tests based on the sample spectrum, and model-based tests.