标题： 坎贝尔平衡方程与非遗传承 Gibbs 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： 本文研究涉及硬核相互作用的吉布斯点过程，其中硬核相互作用不一定是遗传性的。我们首先将Nguyen和Zessin [Math. Nachr. 88 (1979) 105--115]最初提出的著名的Campbell平衡方程推广到非遗传性设定，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程序：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，在此过程中将硬核参数估计值代入。我们证明了该程序在遗传性和非遗传性设定下的相合性。 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 [Math. Nachr. 88 (1979) 105--115], to the non-hereditary setting and consequently introduce 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 estimate the hardcore parameter, then estimate 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 non-hereditary settings.