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

TL;DR

This paper introduces a non-parametric method for estimating the potential function in stationary, isotropic pairwise interaction point processes, proving its consistency under finite-range interactions.

Contribution

It presents a novel non-parametric estimator for the potential function and establishes its consistency and strong consistency for finite-range interactions.

Findings

Estimator is consistent for finite-range potentials

Estimator achieves strong consistency under certain conditions

The relation between potential and Papangelou intensity is clarified

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.