Implementing Approximations to Extreme Eigenvalues and Eigenvalues of Irregular Surface Partitionings for Use in SAR and CAR Models

Abstract

Good approximations of eigenvalues exist for the regular square and hexagonal tessellations. To complement this situation, spatial scientists need good approximations of eigenvalues for irregular tessellations. Starting from known or approximated extreme eigenvalues, the remaining eigenvalues may be in turn approximated. One reason spatial scientists are interested in eigenvalues is because they are needed to calculate the Jacobian term in the autonormal probability model. If eigenvalues are not needed for model fitting, good approximations are needed to give the interval within which the spatial parameter will lie.