非遗传Gibbs点过程的Campbell平衡方程和伪似然估计
Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes
摘要：
在本文中，我们研究吉布斯点过程涉及的硬核相互作用，这不一定是遗传的。我们首先扩展著名的坎贝尔平衡方程，最初提出的阮和Zessin [数学。88（1979）105--115]，并因此引入了可移动点的新概念。一个修改版本的伪似然估计，然后提出，其中涉及这些可移动的点。我们考虑以下两个步骤的估计过程：首先估计硬核参数，然后估计光滑的相互作用参数的伪似然，其中硬核参数估计插件。我们证明了这个过程中的遗传性和非遗传性设置的一致性。
英文摘要：
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.
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