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March, 1992 On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice
Francis Comets
Ann. Statist. 20(1): 455-468 (March, 1992). DOI: 10.1214/aos/1176348532

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.

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Francis Comets. "On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice." Ann. Statist. 20 (1) 455 - 468, March, 1992. https://doi.org/10.1214/aos/1176348532

Information

Published: March, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0787.62100
MathSciNet: MR1150354
Digital Object Identifier: 10.1214/aos/1176348532

Subjects:
Primary: 62F10
Secondary: 60G60 , 62M05 , 82A25

Keywords: Bahadur efficiency , large deviation , Markov random field , maximum likelihood estimator , objective function , pseudolikelihood

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 1 • March, 1992
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