  Spatial prediction is commonly achieved under the assumption of a Gaussian
random field (GRF) by obtaining maximum likelihood estimates of parameters, and
then using the kriging equations to arrive at predicted values. For massive
datasets, fixed rank kriging using the Expectation-Maximization (EM) algorithm
for estimation has been proposed as an alternative to the usual but
computationally prohibitive kriging method. The method reduces computation cost
of estimation by redefining the spatial process as a linear combination of
basis functions and spatial random effects. A disadvantage of this method is
that it imposes constraints on the relationship between the observed locations
and the knots. We develop an alternative method that utilizes the Spatial Mixed
Effects (SME) model, but allows for additional flexibility by estimating the
range of the spatial dependence between the observations and the knots via an
Alternating Expectation Conditional Maximization (AECM) algorithm. Experiments
show that our methodology improves estimation without sacrificing prediction
accuracy while also minimizing the additional computational burden of extra
parameter estimation. The methodology is applied to a temperature data set
archived by the United States National Climate Data Center, with improved
results over previous methodology.
