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首页> 外文期刊>Scandinavian journal of statistics >Hidden Second-order Stationary Spatial Point Processes
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Hidden Second-order Stationary Spatial Point Processes

机译：隐藏的二阶平稳空间点过程

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摘要

In the existing statistical literature, the almost default choice for inference on inhomogeneous point processes is the most well-known model class for inhomogeneous point processes: reweighted second-order stationary processes. In particular, the K-function related to this type of inhomogeneity is presented as the inhomogeneous K-function. In the present paper, we put a number of inhomogeneous model classes (including the class of reweighted second-order stationary processes) into the common general framework of hidden second-order stationary processes, allowing for a transfer of statistical inference procedures for second-order stationary processes based on summary statistics to each of these model classes for inhomogeneous point processes. In particular, a general method to test the hypothesis that a given point pattern can be ascribed to a specific inhomogeneous model class is developed. Using the new theoretical framework, we re-analyse three inhomogeneous point patterns that have earlier been analysed in the statistical literature and show that the conclusions concerning an appropriate model class must be revised for some of the point patterns.
机译：在现有的统计文献中，对非均质点过程进行推理的几乎默认选择是最不均质点过程的模型类：重新加权的二阶平稳过程。特别地，与这种类型的不均匀性有关的K函数被表示为不均匀的K函数。在本文中，我们将许多不均匀的模型类（包括重加权的二阶平稳过程的类）放入了隐藏的二阶平稳过程的通用通用框架中，从而允许对二阶统计推断过程进行转移基于针对这些模型类的不均匀点过程的摘要统计信息的平稳过程。尤其是，开发了一种通用方法来检验以下假设：给定点模式可以归因于特定的不均匀模型类。使用新的理论框架，我们重新分析了统计文献中较早分析的三个不均匀点模式，并表明必须针对某些点模式对有关适当模型类别的结论进行修订。

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