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Functional marked p...
Functional marked point processes : a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data
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- Ghorbani, Mohammad (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden,Luleå tekniska universitet (LTU),Luleå University of Technology (LTU)
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- Cronie, Ottmar (författare)
- Gothenburg University,Göteborgs universitet,Umeå universitet,Institutionen för matematik och matematisk statistik,Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden; Biostatistics, School of Public Health and Community Medicine, Institute of Medicine, University of Gothenburg, Gothenburg, Sweden,Mathematical Statistics,Chalmers tekniska högskola,Chalmers University of Technology,Institutionen för medicin, avdelningen för samhällsmedicin och folkhälsa,Institute of Medicine, School of Public Health and Community Medicine
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- Mateu, Jorge (författare)
- Department of Mathematics, Universitat Jaume I, Castellón, Spain,Universitat Jaume I De Castellon
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- Yu, Jun, 1962- (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden,Umeå University
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(creator_code:org_t)
- 2020-08-25
- 2021
- Engelska.
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Ingår i: Test (Madrid). - : Sociedad de Estadística e Investigación Operativa (Spanish Society of Statistics and Operations Research). - 1133-0686 .- 1863-8260. ; 30:3, s. 529-568
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Abstract
Ämnesord
Stäng
- 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, for example, spatial paths or functions of time. To be able to consider, for example, multivariate FMPPs, we also attach an additional, 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. We further show that various existing stochastic models fit well into the FMPP framework. To be able to carry out nonparametric statistical analyses for FMPPs, we study characteristics such as product densities and Palm distributions, which are the building blocks for many summary statistics. We proceed to defining a new family of summary statistics, so-called weighted marked reduced moment measures, together with their nonparametric estimators, in order to study features of the functional marks. We further show how other summary statistics may be obtained as special cases of these summary statistics. We finally apply these tools to analyse population structures, such as demographic evolution and sex ratio over time, in Spanish provinces.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Nyckelord
- Correlation functional
- Functional data analysis
- Intensity functional
- Nonparametric estimation
- Spatio-temporal geostatistical marking
- Weighted marked reduced moment measure
- matematisk statistik
- Mathematical Statistics
- Correlation functional
- Functional data analysis
- Intensity functional
- Nonparametric estimation
- Spatio-temporal geostatistical marking
- Weighted marked reduced moment measure
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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