  We consider a linear regression model with a spatially correlated error term
on a lattice. When estimating coefficients in the linear regression model, the
generalized least squares estimator (GLSE) is used if the covariance structures
are known. However, the GLSE for large spatial data sets is computationally
expensive, because it involves inverting the covariance matrix of error terms
from each observations. To reduce the computational complexity, we propose a
pseudo best estimator (PBE) using spatial covariance structures approximated by
separable covariance functions. We derive the asymptotic covariance matrix of
the PBE and compare it with those of the least squares estimator (LSE) and the
GLSE through some simulations. Monte Carlo simulations demonstrate that the PBE
using separable covariance functions has superior accuracy to that of the LSE,
which does not contain the information of the spatial covariance structure,
even if the true process has an isotropic Mat\'ern covariance function.
Additionally, our proposed PBE is computationally efficient relative to the
GLSE for large spatial data sets.
