We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.

中文翻译：

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K-和对相关函数的全局强度重新加权估计量

我们介绍了不均匀的新估计ķ -function和空间点进程的对相关函数以及横ķ -function和的二阶强度重新加权的假设下二元空间点进程的横对相关函数平稳性。这些估计器依赖于“全局”归一化因子，该因子依赖于强度函数的聚合，而现有估计器“局部”依赖于各个观察点的强度函数。理论考虑和模拟研究证明了我们新的全局估计器相对于现有局部估计器的优势。