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The discretely observed immigration-death process: Likelihood inference and spatiotemporal applications
Stochastics, CWI, Amsterdam, The Netherlands. (Mathematical Statistics)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)
2016 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 18, 5279-5298 p.Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2016. Vol. 45, no 18, 5279-5298 p.
Keyword [en]
Asymptotic normality, Consistency, Homogenous spatial immigration-death process, Maximum likelihood, Spatial birth–death process, Spatiotemporal growth-interaction process
National Category
Probability Theory and Statistics Forest Science
Research subject
Mathematical Statistics
URN: urn:nbn:se:umu:diva-124363DOI: 10.1080/03610926.2014.942433ISI: 000380898500003OAI: diva2:951068
Swedish Research CouncilSwedish Foundation for Strategic Research
Available from: 2016-08-05 Created: 2016-08-05 Last updated: 2016-09-22Bibliographically approved

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Cronie, OttmarYu, Jun
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