Mathematics > Statistics Theory
[Submitted on 21 Dec 2018 (v1), last revised 29 Oct 2019 (this version, v5)]
Title:Structured space-sphere point processes and $K$-functions
View PDFAbstract:This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb R^d$ (the $d$-dimensional Euclidean space) and $\mathbb S^k$ (the $k$-dimen\-sional sphere). We consider specific classes of models for space-sphere point processes, which are adaptations of existing models for either spherical or spatial point processes. For model checking or fitting, we present the space-sphere $K$-function which is a natural extension of the inhomogeneous $K$-function for point processes on $\mathbb R^d$ to the case of space-sphere point processes. Under the assumption that the intensity and pair correlation function both have a certain separable structure, the space-sphere $K$-function is shown to be proportional to the product of the inhomogeneous spatial and spherical $K$-functions. For the presented space-sphere point process models, we discuss cases where such a separable structure can be obtained. The usefulness of the space-sphere $K$-function is illustrated for real and simulated datasets with varying dimensions $d$ and $k$.
Submission history
From: Heidi Søgaard Christensen [view email][v1] Fri, 21 Dec 2018 07:56:04 UTC (3,711 KB)
[v2] Wed, 2 Jan 2019 11:01:42 UTC (3,696 KB)
[v3] Wed, 20 Mar 2019 13:47:10 UTC (3,696 KB)
[v4] Tue, 21 May 2019 07:44:23 UTC (3,696 KB)
[v5] Tue, 29 Oct 2019 18:18:38 UTC (3,696 KB)
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