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Functional marked point processes: Unifying spatio-temporal frameworks and analysing spatially 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)
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (Mathematical Statistics)ORCID-id: 0000-0001-5673-620X
Department of Mathematics, Universitat Jaume I, Castellón, Spain.
2019 (Engelska)Ingår i: Statistical Analysis for Space-Time Data: Pragramme and Abstract Book, Eurpean Courses in Advanced Statistics (ECAS) , 2019, s. 7-7Konferensbidrag, Poster (med eller utan abstract) (Refereegranskat)
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 additionally, Euclidean, mark to each point. We indicate how the FMPP framework quite naturally connects the point process framework with both the functional data analysis framework and the geostatistical framework; in particular we define spatio-temporal geostatistical marking for point processes. We further show that various existing stochastic models fit well into the FMPP framework, in particular marked point processes with real valued marks. To be able to carry out non-parametric statistical analyses for functional marked point patterns, we study characteristics such as product densities and Palm distributions, which are the building blocks for summary statistics such as marked inhomogeneous J-functions and our so-called K-functionals. We finally apply these statistical tools to analyse a few different functional marked point patterns.

Ort, förlag, år, upplaga, sidor
Eurpean Courses in Advanced Statistics (ECAS) , 2019. s. 7-7
Nyckelord [en]
C`adl`ag stochastic process, Correlation functional, Functional marked point process, Intensity functional, Marked inhomogeneous K-functional, Spatiotemporal geostatistical marking
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-161564OAI: oai:DiVA.org:umu-161564DiVA, id: diva2:1337093
Konferens
ECAS 2019 on Statistical Analysis for Space-Time Data. Lisboa, Portugal, July 15-17, 2019
Projekt
Large scale analysis of tree growth in space and time under changing climate conditions
Forskningsfinansiär
Kempestiftelserna, SMK-1750Tillgänglig från: 2019-07-11 Skapad: 2019-07-11 Senast uppdaterad: 2021-10-19Bibliografiskt granskad

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Cronie, OttmarGhorbani, MohammadYu, Jun

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Totalt: 261 träffar
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