Weak and Strong Consistency of non-parametric estimate of potential function for stationary and isotropic pairwise interaction point process

Abstract: A method is proposed for estimating the potential function of a non-parametric estimator for stationary and isotropic pairwise interaction point process. The relation between a pair potential and the corresponding Papangelou conditional intensity is considered. Consistency and strong consistency of non-parametric estimate are proved in case of finite-range interaction potential.