Fitting spatial regressions to large datasets using unilateral approximations

Maximum likelihood estimation of a spatial model typically requires a sizeable\r\ncomputational capacity, even in relatively small samples, and becomes unfeasible in\r\nvery large datasets. The unilateral approximation approach to spatial models estimation\r\n(suggested in Besag, 1974) provides a viable alternative to maximum likelihood\r\nestimation that reduces substantially computing time and the storage required.\r\nIn this paper we extend the method, originally proposed for conditionally specified\r\nprocesses, to simultaneous and to general bilateral spatial processes. We prove the\r\nestimators’ consistency and studytheir finite-sample propertiesvia Monte Carlo simulations.