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The discretely observed immigration-death process: Likelihood inference and spatiotemporal applications
Stochastics, CWI, Amsterdam, The Netherlands. (Mathematical Statistics)
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (Mathematical Statistics)
2016 (engelsk)Inngår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, nr 18, s. 5279-5298Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.

sted, utgiver, år, opplag, sider
Taylor & Francis Group, 2016. Vol. 45, nr 18, s. 5279-5298
Emneord [en]
Asymptotic normality, Consistency, Homogenous spatial immigration-death process, Maximum likelihood, Spatial birth–death process, Spatiotemporal growth-interaction process
HSV kategori
Forskningsprogram
matematisk statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-124363DOI: 10.1080/03610926.2014.942433ISI: 000380898500003OAI: oai:DiVA.org:umu-124363DiVA, id: diva2:951068
Forskningsfinansiär
Swedish Research CouncilSwedish Foundation for Strategic Research Tilgjengelig fra: 2016-08-05 Laget: 2016-08-05 Sist oppdatert: 2018-06-07bibliografisk kontrollert

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