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Resample-smoothing of Voronoi intensity estimators
Institute of New Imaging Technologies (INIT), University Jaume I, Castellon, Spain.ORCID iD: 0000-0003-3905-4498
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-6721-8608
Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.ORCID iD: 0000-0002-6675-533X
Université Paris Descartes, Sorbonne Paris Cité, Paris, France.
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2019 (English)In: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 29, no 5, p. 995-1010Article in journal (Refereed) Epub ahead of print
Abstract [en]

Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their major drawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed point pattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additional smoothing operation to the Voronoi estimator, based on resampling the point pattern by independent random thinning. Through a simulation study we show that our resample-smoothing technique improves the estimation substantially. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of smoothing to apply. Finally we apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern).

Place, publisher, year, edition, pages
Springer, 2019. Vol. 29, no 5, p. 995-1010
Keywords [en]
Adaptive intensity estimation, Complete separable metric space, Independent thinning, Point process, Resampling, Voronoi intensity estimator
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics; Mathematics; Statistics
Identifiers
URN: urn:nbn:se:umu:diva-152073DOI: 10.1007/s11222-018-09850-0ISI: 000482225200009Scopus ID: 2-s2.0-85060327193OAI: oai:DiVA.org:umu-152073DiVA, id: diva2:1251022
Available from: 2018-09-25 Created: 2018-09-25 Last updated: 2019-10-31Bibliographically approved

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Cronie, Ottmar

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Moradi, M. MehdiCronie, OttmarRubak, EgeMateu, JorgeBaddeley, Adrian
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