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Second-order analysis of marked inhomogeneous spatio-temporal point processes: applications to earthquake data
Department of Biosciences and Nutrition, Karolinska Institutet, Stockholm, Sweden.ORCID iD: 0000-0001-8117-3461
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-6721-8608
Department of Statistics and Operations Research, University of Valencia, Valencia, Spain.
2018 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469Article in journal (Refereed) Epub ahead of print
Abstract [en]

To analyse interactions in marked spatio-temporal point processes (MSTPPs), we introduce marked second-order reduced moment measures and K-functions for inhomogeneous second-order intensity reweighted stationary MSTPPs. These summary statistics, which allow us to quantify dependence between different mark-based classifications of the points, are depending on the specific mark space and mark reference measure chosen. Unbiased and consistent minus-sampling estimators are derived for all statistics considered and a test for random labelling is indicated. In addition, we treat Voronoi intensity estimators for MSTPPs. These new statistics are finally employed to analyse an Andaman sea earthquake data set.

Place, publisher, year, edition, pages
2018.
Keywords [en]
adaptive intensity estimation, earthquakes, marked inhomogeneous spatiotemporal point process, marked (second-order) intensity-reweighted stationarity, marked spatiotemporal K-function, marked spatiotemporal second-order reduced moment measure
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-153405DOI: 10.1111/sjos.12367OAI: oai:DiVA.org:umu-153405DiVA, id: diva2:1264175
Available from: 2018-11-19 Created: 2018-11-19 Last updated: 2019-04-04

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Cronie, Ottmar

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