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J-function for Inhomogeneous Spatio-temporal Point Processes
CWI, Amsterdam, The Netherlands.ORCID iD: 0000-0002-6721-8608
CWI, Amsterdam, The Netherlands.
2015 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 42, no 2, 562-579 p.Article in journal (Refereed) Published
Abstract [en]

We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.

Place, publisher, year, edition, pages
John Wiley & Sons, 2015. Vol. 42, no 2, 562-579 p.
Keyword [en]
inhomogeneous spatio-temporal point process, intensity-reweighted moment stationarity, J-function, K-function, location-dependent thinning of hard core model, log-Gaussian Cox process, n-point correlation function, Papangelou conditional intensity, Poisson process, (reduced Palm measure) generating functional
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-114485DOI: 10.1111/sjos.12123ISI: 000353543300016OAI: oai:DiVA.org:umu-114485DiVA: diva2:896221
Available from: 2016-01-20 Created: 2016-01-20 Last updated: 2016-02-25Bibliographically approved

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Cronie, Ottmar
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