On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice
The Annals of Statistics · 1992 · Volume 20 · Issue 1
Abstract
We prove strong consistency of a class of maximum objective estimators for exponential parametric families of Markov random fields on $\mathbb{Z}^d$, 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.
Keywords
60G60; 62F10; 62M05; 82A25; Bahadur efficiency; large deviation; Markov random field; maximum likelihood estimator; objective function; pseudolikelihood;
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