Preprint #96-7
Asymptotic Properties of Maximum Likelihood Estimators
for Partially Ordered Markov Models
by
Hsin-cheng Huang and Noel Cressie
Abstract
Partially ordered Markov models (POMMs) are Markov random fields (MRF)
with neighborhood structures derivable from an associated partially
ordered set. The most attractive feature of POMMs is that their joint
distributions can be written in closed and product form. Therefore,
simulation and maximum likelihood estimation for the models is quite
straightforward, which is not the case in general for MRF models. In
this article, we shall use a martingale approach to derive the asymptotic
vproperties of maximum likelihood estimators (MLEs) for POMMs. We shall
prove that, under regularity conditions that include Dobrushin's
condition for spatial mixing, the MLE is consistent, asymptotically
normal, and also asymptotically efficient.
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University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.