an:04094621
Zbl 0668.62059
Jan??ura, Martin
Estimating interactions in binary lattice data with nearest-neighbor property
EN
Kybernetika 23, 136-142 (1987).
00153103
1987
j
62M05 62M99 82B30 80A10
two-state Markov stationary Gibbs random field; empirical minimum estimator
The estimation problem for the interaction parameter \(U\in R^ 3\) of a two-state Markov stationary Gibbs random field on \(({\mathbb{Z}}^+)^ 2\) is considered. Let \(x_{D(m,n)}\) be an observation of the field on a rectangular domain D(m,n) of size \(m\times n\), and put \(\hat U_{m,n}\) for the empirical minimum estimator for U from theorem 3.12 of the well- known book of \textit{D. Ruelle} [Thermodynamic formalism. The mathematical structures of classical equilibrium. Statistical mechanics. (1978; Zbl 0401.28016)].
Theorem: \(\hat U_{m,n}\to U\) almost sure for m,n\(\to \infty\). An approximate calculation method for the values of \(\hat U_{m,n}\) through \(x_{D(m,n)}\), and an example are given.
E.I.Trofimov
Zbl 0401.28016