平稳标记Gibbs点过程的Takacs Fiksel方法
Takacs Fiksel method for stationary marked Gibbs point processes
摘要：
本文研究了平稳标记Gibbs点过程分布参数的估计方法。这个过程，被称为Takacs-Fiksel方法，是基于估计的左，右手边的Georgii-Nguyen-Zessin公式，并导致家庭的估计，由于可能的选择检验函数。我们提出了几个例子说明这个过程的兴趣和灵活性。我们还提供了充分条件的基础上的模型和检验函数，以获得渐近性质（一致性和渐近正态性）的估计。不同的假设进行了讨论指数族模型和一大类检验函数。一个简短的模拟研究，提出了评估的方法和渐近结果的正确性。
英文摘要：
This paper studies a method to estimate the parameters governing the distribution of a stationary marked Gibbs point process. This procedure, known as the Takacs-Fiksel method, is based on the estimation of the left and right hand sides of the Georgii-Nguyen-Zessin formula and leads to a family of estimators due to the possible choices of test functions. We propose several examples illustrating the interest and flexibility of this procedure. We also provide sufficient conditions based on the model and the test functions to derive asymptotic properties (consistency and asymptotic normality) of the resulting estimator. The different assumptions are discussed for exponential family models and for a large class of test functions. A short simulation study is proposed to assess the correctness of the methodology and the asymptotic results.
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