Fitting spatial regressions to large datasets using unilateral approximations

Maximum likelihood estimation of a spatial model typically requires a sizeable computational capacity, even in relatively small samples, and becomes unfeasible in very large datasets. The unilateral approximation approach to spatial models estimation (suggested in Besag, 1974) provides a viable alternative to maximum likelihood estimation that reduces substantially computing time and the storage required. In this paper we extend the method, originally proposed for conditionally specified processes, to simultaneous and to general bilateral spatial processes over rectangular lattices. We prove the estimators' consistency and study their finite-sample properties via Monte Carlo simulations.