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Ghorbani, Mohammad
Publications (2 of 2) Show all publications
Cronie, O., Ghorbani, M., Mateu, J. & Yu, J. (2019). Functional marked point processes: A natural structure to unify spatio-temporal frameworks and to analyse dependent functional data.
Open this publication in new window or tab >>Functional marked point processes: A natural structure to unify spatio-temporal frameworks and to analyse dependent functional data
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.

Publisher
p. 44
Keywords
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:nbn:se:umu:diva-165644 (URN)
Projects
Large scale analysis of tree growth in space and time under changing climate conditions
Funder
The Kempe Foundations, SMK-1750
Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2019-12-03
Cronie, O., Ghorbani, M., Yu, J. & Mateu, J. (2019). Functional marked point processes: Unifying spatio-temporal frameworks and analysing spatially dependent functional data. In: Statistical Analysis for Space-Time Data: Pragramme and Abstract Book. Paper presented at ECAS 2019 on Statistical Analysis for Space-Time Data. Lisboa, Portugal, July 15-17, 2019 (pp. 7-7). Eurpean Courses in Advanced Statistics (ECAS)
Open this publication in new window or tab >>Functional marked point processes: Unifying spatio-temporal frameworks and analysing spatially dependent functional data
2019 (English)In: Statistical Analysis for Space-Time Data: Pragramme and Abstract Book, Eurpean Courses in Advanced Statistics (ECAS) , 2019, p. 7-7Conference paper, Poster (with or without abstract) (Refereed)
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.

Place, publisher, year, edition, pages
Eurpean Courses in Advanced Statistics (ECAS), 2019
Keywords
C`adl`ag stochastic process, Correlation functional, Functional marked point process, Intensity functional, Marked inhomogeneous K-functional, Spatiotemporal geostatistical marking
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-161564 (URN)
Conference
ECAS 2019 on Statistical Analysis for Space-Time Data. Lisboa, Portugal, July 15-17, 2019
Projects
Large scale analysis of tree growth in space and time under changing climate conditions
Funder
The Kempe Foundations, SMK-1750
Available from: 2019-07-11 Created: 2019-07-11 Last updated: 2020-02-07Bibliographically approved
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