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Resample-smoothing ...
Resample-smoothing of Voronoi intensity estimators
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- Moradi, M. Mehdi (författare)
- Institute of New Imaging Technologies (INIT), University Jaume I, Castellon, Spain,Umeå universitet,Umeå University
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- Cronie, Ottmar (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University
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- Rubak, Ege (författare)
- Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark,Aalborg Universitet,Aalborg University
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- Lachieze-Rey, Raphael (författare)
- Université Paris Descartes, Sorbonne Paris Cité, Paris, France
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- Mateu, Jorge (författare)
- Department of Mathematics, University Jaume I, Castellon, Spain,Universitat Jaume I De Castellon
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- Baddeley, Adrian (författare)
- Department of Mathematics and Statistics, Curtin University, Perth, Australia,Curtin University
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(creator_code:org_t)
- 2019-01-19
- 2019
- Engelska.
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Ingår i: Statistics and computing. - : Springer. - 0960-3174 .- 1573-1375. ; 29:5, s. 995-1010
- Relaterad länk:
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https://doi.org/10.1...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- 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).
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Nyckelord
- Adaptive intensity estimation
- Complete separable metric space
- Independent thinning
- Point process
- Resampling
- Voronoi intensity estimator
- matematisk statistik
- Mathematical Statistics
- Mathematics
- matematik
- Statistics
- statistik
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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