Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions

Summary A parametric model of planar point patterns in a bounded region is constructed using grand canonical Gibbsian point processes with soft-core potential functions. A simple and explicit condition that this model becomes a uniform locally asymptotic normal (ULAN) family will be given. From this result we can conclude that the maximum likelihood estimator of the potential function is asymptotically efficient for a wide class of loss functions.