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Hidden Second-order Stationary Spatial Point Processes

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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 reanalyse 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.
Original languageEnglish
JournalScandinavian Journal of Statistics
Volume43
Issue2
Pages (from-to)455-475
Number of pages21
ISSN0303-6898
DOIs
Publication statusPublished - 14 May 2016

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