Second-Order Analysis of Inhomogeneous Spatial Point Processes With Proportional Intensity Functions
Second-Order Analysis of Inhomogeneous Spatial Point Processes With Proportional Intensity Functions
复制标题
具有比例强度函数的非齐次空间点过程的二阶分析
DOI：
10.1198/016214508000000391
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发表时间：
2008
影响因子：
3.7
通讯作者：
C. Beale
中科院分区：
文献类型：
--
作者：
Yongtao Guan;R. Waagepetersen;C. Beale
我们考虑了强度函数共享一个公共乘法项的空间点过程对。我们介绍了两种新的方法来估计对相关函数的点过程之一，通过治疗其他作为基线，以便占未指定的部分的强度函数。第一种方法是基于非参数核平滑，而第二种方法使用条件似然估计方法来拟合对相关函数的参数模型。所提出的方法的一个很大的优点是，它们不需要经常困难的估计的强度函数的未指定的部分。我们建立的一致性估计，并讨论如何参数估计可以应用于模型诊断和推断回归参数的强度函数。我们提出的程序，以两个空间点模式的鸟类在英国的空间分布。在1990年和2004年，
We consider pairs of spatial point processes with intensity functions sharing a common multiplicative term. We introduce two novel approaches to estimating the pair correlation function for one of the point processes by treating the other as a baseline so as to account for the unspecified part of the intensity functions. The first approach is based on nonparametric kernel-smoothing, whereas the second approach uses a conditional likelihood estimation approach to fit a parametric model for the pair correlation function. A great advantage of the proposed methods is that they do not require the often difficult estimation of the unspecified part of the intensity functions. We establish the consistency of the resulting estimators and discuss how the parametric estimator can be applied in model diagnostics and inference on regression parameters for the intensity functions. We apply the proposed procedures to two spatial point patterns regarding the spatial distributions of birds in the U.K.'s Peak District in 1990 and 2004.