Resample-smoothing of Voronoi intensity estimators
Scholar | Other documents of the author: Moradi, Mohammad Mehdi; Cronie, Ottmar; Rubak, Ege; Lachieze-Rey, Raphael; Mateu, Jorge
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TitleResample-smoothing of Voronoi intensity estimators
Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimateat a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing ... [+]
Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimateat a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their majordrawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed pointpattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additionalsmoothing operation to the Voronoi estimator, based on resampling the point pattern by independent random thinning. Througha simulation study we show that our resample-smoothing technique improves the estimation substantially. In addition, westudy statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validationapproach to choose the amount of smoothing to apply. Finally we apply our proposed intensity estimation scheme to twodatasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern). [-]
Investigation projectM.M. Moradi gratefully acknowledgesfunding from the European union through the GEO-C project (H2020-MSCA-ITN-2014, Grant Agreement Number 642332,http://www.geo-c.eu/); J. Mateu is partially funded by Grants MTM2016-78917-R fromthe Spanish Ministry of Science and Education, and P1-1B2015-40from University of Jaume I. Ege Rubak was supported by The DanishCouncil for Independent Research|Natural Sciences, Grant DFF—7014–00074 “Statistics for point processes in space and beyond”; bya six-month visiting position at Curtin University; and by the Centrefor Stochastic Geometry and Advanced Bioimaging, funded by Grant8721 from the Villum Foundation. Adrian Baddeley was funded bythe Australian Research Council, Discovery Grants DP1301002322and DP130104470.
Bibliographic citationMORADI, M. Mehdi, et al. Resample-smoothing of Voronoi intensity estimators. Statistics and Computing, 2018, p. 1-16
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