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Functional marked point processes: A natural structure to unify spatio-temporal frameworks and to analyse dependent functional data
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (Mathematical Statistics)
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (Mathematical Statistics)
Department of Mathematics, Universitat Jaume I, Castellón, Spain.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (Mathematical Statistics)ORCID-id: 0000-0001-5673-620x
2019 (engelsk)Manuskript (preprint) (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
2019. , s. 44
Emneord [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
HSV kategori
Forskningsprogram
matematisk statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-165644OAI: oai:DiVA.org:umu-165644DiVA, id: diva2:1374705
Prosjekter
Large scale analysis of tree growth in space and time under changing climate conditions
Forskningsfinansiär
The Kempe Foundations, SMK-1750Tilgjengelig fra: 2019-12-02 Laget: 2019-12-02 Sist oppdatert: 2019-12-03

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arXiv:1911.13142

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