Abstract
We prove that the Maximum Likelihood and Pseudo-likelihood estimators for the parameters of Gibbs distributions (equivalently Markov Random Fields) over ℤd, d≥l, are consistent even at points of “first” or “higher-order” phase transitions. The distributions are parametrized by points in a finite-dimensional Euclidean space ℝm, m≥l, and the single spin state space is either a finite set or a compact metric space. Also, the underlying interactions need not be of finite range.
To appear in Proceedings of the Workshop on Stochastic Differential Systems with Applications in Electrical/Computer Engineering, Control Theory, and Operations Research. June 9–19, 1986, Institute for Mathematics and Its Applications, University of Minnesota.
Partially supported by ARO DAAG-29–83-K-0116, and NSF Grant DMS 85-16230.
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Gidas, B. (1988). Consistency of Maximum Likelihood and Pseudo-Likelihood Estimators for Gibbs Distributions. In: Fleming, W., Lions, PL. (eds) Stochastic Differential Systems, Stochastic Control Theory and Applications. The IMA Volumes in Mathematics and Its Applications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8762-6_10
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