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Locally asymptotic normality of Gibbs models on a lattice. (English) Zbl 0546.60099
An attractive stochastic model for spatial data is the Gibbs model which has its origin in statistical physics (random fields). The most important statistical problem about the Gibbs models is the estimation of potential functions which describe the Gibbs distributions. Although in practice data are observed only in a finite region, we take an asymptotic viewpoint, that is, we let the regions expand.
The main result of this paper is to show that, under several assumptions, Gibbs models are locally asymptotically normal in the sense of Le Cam. By this result and some known results, the author then shows that the maximum likelihood estimators have an optimal property. An estimation procedure based on the moment method is also proposed in the paper.
Reviewer: M.Chen

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
62E20 Asymptotic distribution theory in statistics
62M09 Non-Markovian processes: estimation
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