Asymptotic expansions for statistics computed from spatial data

Abstract

The Edgeworth expansions for dependent data are generalized to the context of spatial patterns, with the aim of obtaining asymptotic expansions which approximate the distribution of statistics computed from spatial data, generated by a weakly dependent coverage process. In particular, the case of estimating the expected proportion (its porosity) of a region that is not covered by the process is treated in detail and explicit formulae are given in the context of a Boolean model, assuming that the random sets generating the model are essentially bounded and satisfy a version of Cramér’s condition.