Pseudo-Likelihood estimation for non-hereditary Gibbs point processes

We deal with the parametric estimation of the potential interaction in non-hereditary Gibbs point processes. We use a modified version of the pseudo-likelihood estimator and we prove its consistency. It was needed to extend the famous equilibrium Campbell equation, initially due to Nguyen and Zessin, to the non-hereditary setting. Our procedure allows to estimate both the hardcore paramaters and the smooth interaction parameters.