Regression Models with Spatially Correlated Errors

In this article we consider regression models for two-dimensional spatial data when the errors follow a spatial unilateral first-order autoregressive moving average (ARMA) model studied by Basu and Reinsel. We give details on the convenient computation of the generalized least squares (GLS) estimator of the regression parameters in the presence of spatially correlated errors, and compare the GLS estimator to the ordinary least squares (OLS) estimator in some special cases. We also consider the restricted maximum likelihood estimators of the spatial correlation model parameters, which may be preferred over the maximum likelihood estimators. For the special case of the spatial unilateral first-order AR model, details of the maximum likelihood as well as the restricted maximum likelihood estimation are given. A numerical example is presented to illustrate the methods.