  Additive spatial statistical models with weakly stationary process
assumptions have become standard in spatial statistics. However, one
disadvantage of such models is the computation time, which rapidly increases
with the number of data points. The goal of this article is to apply an
existing subsampling strategy to standard spatial additive models and to derive
the spatial statistical properties. We call this strategy the ''spatial data
subset model'' (SDSM) approach, which can be applied to big datasets in a
computationally feasible way. Our approach has the advantage that one does not
require any additional restrictive model assumptions. That is, computational
gains increase as model assumptions are removed when using our model framework.
This provides one solution to the computational bottlenecks that occur when
applying methods such as Kriging to ''big data''. We provide several properties
of this new spatial data subset model approach in terms of moments, sill,
nugget, and range under several sampling designs. An advantage of our approach
is that it subsamples without throwing away data, and can be implemented using
datasets of any size that can be stored. We present the results of the spatial
data subset model approach on simulated datasets, and on a large dataset
consists of 150,000 observations of daytime land surface temperatures measured
by the MODIS instrument onboard the Terra satellite.
