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.
Publié le : 1992-03-14
Classification:
Maximum likelihood estimator,
pseudolikelihood,
Markov random field,
objective function,
Bahadur efficiency,
large deviation,
62F10,
62M05,
82A25,
60G60
@article{1176348532,
author = {Comets, Francis},
title = {On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 455-468},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348532}
}
Comets, Francis. On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice. Ann. Statist., Tome 20 (1992) no. 1, pp. 455-468. http://gdmltest.u-ga.fr/item/1176348532/