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Functional marked point processes: A natural structure to unify spatio-temporal frameworks and to analyse dependent functional data
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)
Department of Mathematics, Universitat Jaume I, Castellón, Spain.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620x
2019 (English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent e.g. spatial paths or functions of time. To be able to consider e.g. multivariate FMPPs, we also attach an additional, Euclidean, mark to each point. We indicate how FMPPs quite naturally connect the point process framework with both the functional data analysis framework and the geostatistical framework. We further show that various existing models fit well into the FMPP framework. In addition, we introduce a new family of summary statistics, weighted marked reduced moment measures, together with their non-parametric estimators, in order to study features of the functional marks. We further show how they generalise other summary statistics and we finally apply these tools to analyse population structures, such as demographic evolution and sex ratio over time, in Spanish provinces.

Place, publisher, year, edition, pages
2019. , p. 44
Keywords [en]
Correlation functional, Functional data analysis, Intensity functional, Marked point process, Nonparametric estimation, Palm distribution, Population growth, Spatio-temporal geostatistical marking, Weighted marked reduced moment measure
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-165644OAI: oai:DiVA.org:umu-165644DiVA, id: diva2:1374705
Projects
Large scale analysis of tree growth in space and time under changing climate conditions
Funder
The Kempe Foundations, SMK-1750Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2019-12-03

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arXiv:1911.13142

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Cronie, OttmarGhorbani, MohammadYu, Jun

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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