论文标题
局部不均匀加权摘要统计数据，用于标记的点过程
Local inhomogeneous weighted summary statistics for marked point processes
论文作者
论文摘要
我们介绍了一个局部不均匀的标记加权汇总统计数据的家庭，该统计数据是二大或更高的命令，用于一般标记的点过程。根据如何指定涉及的权重函数，这些摘要统计信息捕获了不同种类的局部依赖结构。我们首先得出了一些基本属性，并展示了如何使用这些新的统计工具来构建（标记）点过程的大多数现有摘要统计信息。然后，我们提出了随机标记的局部测试。此过程使我们能够识别未达到随机标记假设的点，因此是区域，例如，当（函数）标记在空间上依赖时。通过模拟研究，我们表明该测试能够检测到与随机标记的局部偏差。我们还为地震点模式提供了一种应用，具有地震波形给出的功能标记。
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture different kinds of local dependence structures. We first derive some basic properties and show how these new statistical tools can be used to construct most existing summary statistics for (marked) point processes. We then propose a local test of random labelling. This procedure allows us to identify points, and consequently regions, where the random labelling assumption does not hold, e.g.~when the (functional) marks are spatially dependent. Through a simulation study we show that the test is able to detect local deviations from random labelling. We also provide an application to an earthquake point pattern with functional marks given by seismic waveforms.
