Model Fitting and Inference Issues For Analyzing Large Spatial Data Sets


Researchers in diverse areas such as climatology, environmental
health, and ecology are facing the task of analyzing increasingly
large spatial data sets. For the usual Gaussian spatial process
modeling of geographically referenced data, likelihood based inference
becomes very demanding, or even infeasible as it involves computing
quadratic forms and determinants associated with a large covariance
matrix. We develop a finite sum process approximation model, which is
conceptually simple and routine to implement. Examples are presented
to illustrate the method. Additionally, we observe that some
parameters in spatial models are not well estimated even with
relatively large number of samples. Motivated by that, we consider
issues in spatial asymptotics.  We discuss consistency and asymptotic
properties of the estimators for parameters in spatial models.