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 model estimation (suggested in Besag 1974 Besag, J. E. 1974. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B (Methodological) 36 (2):192–236. [Web of Science ®], , [Google Scholar] ) provides a viable alternative to maximum likelihood estimation that reduces substantially the computing time and the storage required. In this article, 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.