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Asymptotic Properties Of Maximum (Composite) Likelihood Estimators For Partially Ordered Markov Models, Hsin-Cheng Huang, Noel A. Cressie

Professor Noel Cressie

Partially ordered Markov models (POMMs) are Markov random fields (MRFs) 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 practice, one often has to modify the likelihood to account for edge components; the resulting composite likelihood for POMMs is similarly straightforward to maximize. In this article, we use a martingale approach to derive the asymptotic properties of …