Kybernetika 50 no. 6, 883-895, 2014

An efficient estimator for Gibbs random fields

Martin JanžuraDOI: 10.14736/kyb-2014-6-0883


An efficient estimator for the expectation $\int f \d P$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer \cite{greenwood_wefelmeyer_1999}, and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.


Gibbs random field, efficient estimator, empirical estimator


62F12, 62M40


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