平稳标记Gibbs点过程的Resistance和拟合优度检验
Residuals and goodness-of-fit tests for stationary marked Gibbs point processes
摘要：
残差检验是研究参数模型对数据平差质量的基本步骤。对于空间点过程，Baddeley等人（2005）最近提出了残差的概念，作为标记Gibbs点过程的{ \it Campbell平衡}方程的经验对应。本文主要研究平稳标记Gibbs点过程，并讨论这类过程残差的渐近性质。特别地，得到了包括经典残差（原始残差、逆残差、Pearson残差）在内的广泛一类残差的相合性和渐近正态性.基于这些渐近结果，我们定义了理论上控制I型误差的拟合优度检验。这些测试之一构成了广泛用于测试齐次泊松点过程的原假设的样方计数测试的扩展。
英文摘要：
The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. (2005) as an empirical counterpart of the {\it Campbell equilibrium} equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs point processes and deals with asymptotic properties of residuals for such processes. In particular, the consistency and the asymptotic normality are obtained for a wide class of residuals including the classical ones (raw residuals, inverse residuals, Pearson residuals). Based on these asymptotic results, we define goodness-of-fit tests with Type-I error theoretically controlled. One of these tests constitutes an extension of the quadrat counting test widely used to test the null hypothesis of a homogeneous Poisson point process.
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