Nonparametric Estimation for Gibbs Random Fields Specified Through One‐Point Systems

The problem of nonparametric estimation for Gibbs random fields is considered. The field is supposed to be specified through a translation invariant quasilocal one‐point system. An estimator of one‐point system is constructed by the method of sieves, and its exponential and L^p consistencies are proved in different setups. The results hold regardless of non‐uniqueness and translation invariance breaking. This revised version was published online in June 2006 with corrections to the Cover Date.