Resampling configurations of points through coding schemes

Abstract

We consider nonparametric variance estimation problems in Gibbs point processes admitting the Dobrushin uniqueness condition. Gibbs point processes can be viewed as Gibbs random fields, and vice versa. Nonparametric estimates are obtained from an original sample, which consists of fixed, conditionally independent subregions partitioning the observed region, where a configuration of points lies. Each subregion consists of adjacent rectangles situated around specific sites in a Gibbs random field. We resample these subregions, completely avoiding Monte Carlo simulation.