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Ghorbani, Mohammad

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### Cronie, Ottmar

### Ghorbani, Mohammad

### Mateu, Jorge

### Yu, Jun

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##### Abstract [en]

##### 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)
#####

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##### 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

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Department of Mathematics, Universitat Jaume I, Castellón, Spain.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.

Open this publication in new window or tab >>Functional marked point processes: Unifying spatio-temporal frameworks and analysing spatially dependent functional data### Cronie, Ottmar

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Ghorbani, Mohammad

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Mateu, Jorge

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 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]

##### 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
#####

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#####

##### 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

Department of Mathematics, Universitat Jaume I, Castellón, Spain.

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.