On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice

We prove strong consistency of a class of maximum objective estimators for exponential parametric families of Markov random fields on Zᵈ, including both maximum likelihood and pseudolikelihood estimators, using large deviation estimates. We also obtain the optimality property for the maximum likelihood estimator in the sense of Bahadur.