Model-based tests for simplification of lattice processes

Abstract

Separable processes represent a convenient class of models for data collected on a regular rectangular lattice. Three model-based tests, for testing separability and testing axial symmetry and separability together, are presented. These are shown to be much more powerful than existing model-free tests using the sample periodogram, provided the model assumptions hold. A simulation study also suggests that these tests are not very sensitive to small departures from the assumed process