Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data

Mohammad Ghorbani, Ottmar Cronie (), Jorge Mateu and Jun Yu
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Mohammad Ghorbani: Umeå University
Ottmar Cronie: Umeå University
Jorge Mateu: University Jaume I
Jun Yu: Umeå University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 3, No 1, 529-568

Abstract: Abstract 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.

Keywords: Correlation functional; Functional data analysis; Intensity functional; Nonparametric estimation; Spatio-temporal geostatistical marking; Weighted marked reduced moment measure; 60G55; 62H11; 60G57; 62R10; 86A32; 60D05; 62M30; 62M40; 62M09; 62M99; 62G05; 62G10 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11749-020-00730-2

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