Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range

TL;DR

This paper proposes a semi-parametric estimator for the Poisson intensity in stationary Gibbs point processes, demonstrating its consistency, normality, and finite-sample performance through theoretical analysis and simulations.

Contribution

It introduces a new semi-parametric estimator for the intensity parameter, with proven theoretical properties and practical evaluation.

Findings

Estimator is strongly consistent and asymptotically normal.

Simulation results show good finite-sample performance.

Applicable to a broad class of Gibbs models.

Abstract

We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and asymptotic normality. We also consider its finite-sample properties in a simulation study.