标题： 坎贝尔平衡方程和非遗传吉布斯点过程的伪似然估计 显示英文标题

标题： Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes

摘要： 在本文中，我们研究涉及非继承性硬核相互作用的吉布斯点过程。我们首先将由Nguyen和Zessin（\cite{NZ}）最初提出的著名坎贝尔平衡方程扩展到非继承性设置，并由此引入了可移除点的新概念。然后提出了一种修改后的伪似然估计量，该估计量涉及这些可移除点。我们考虑以下两步估计过程：首先估计硬核参数，然后通过伪似然估计平滑相互作用参数，其中硬核参数估计量被代入。我们在继承性和非继承性设置中都证明了该过程的一致性。 显示英文摘要

摘要： In this paper, we study Gibbs point processes involving a hardcore interaction which is not necessarily hereditary. We first extend the famous Campbell equilibrium equation, initially proposed by Nguyen and Zessin (\cite{NZ}), to the non-hereditary setting and introduce consequently the new concept of removable points. A modified version of the pseudo-likelihood estimator is then proposed, which involves these removable points. We consider the following two-step estimation procedure: First estimating the hardcore parameter, then estimating the smooth interaction parameter by pseudo-likelihood, where the hardcore parameter estimator is plugged in. We prove the consistency of this procedure in both the hereditary and the non-hereditary setting.