Resample-smoothing of Voronoi intensity estimators
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-s...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
| Published: |
Springer Science+Business Media BV
2019
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| Online Access: | http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/74457 |
| _version_ | 1848763280227565568 |
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| author | Moradi, M. Cronie, O. Rubak, E. Lachieze-Rey, R. Mateu, J. Baddeley, Adrian |
| author_facet | Moradi, M. Cronie, O. Rubak, E. Lachieze-Rey, R. Mateu, J. Baddeley, Adrian |
| author_sort | Moradi, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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). |
| first_indexed | 2025-11-14T11:00:57Z |
| format | Journal Article |
| id | curtin-20.500.11937-74457 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:00:57Z |
| publishDate | 2019 |
| publisher | Springer Science+Business Media BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-744572022-10-12T02:42:50Z Resample-smoothing of Voronoi intensity estimators Moradi, M. Cronie, O. Rubak, E. Lachieze-Rey, R. Mateu, J. Baddeley, Adrian 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). 2019 Journal Article http://hdl.handle.net/20.500.11937/74457 10.1007/s11222-018-09850-0 http://purl.org/au-research/grants/arc/DP130104470 http://creativecommons.org/licenses/by/4.0/ Springer Science+Business Media BV fulltext |
| spellingShingle | Moradi, M. Cronie, O. Rubak, E. Lachieze-Rey, R. Mateu, J. Baddeley, Adrian Resample-smoothing of Voronoi intensity estimators |
| title | Resample-smoothing of Voronoi intensity estimators |
| title_full | Resample-smoothing of Voronoi intensity estimators |
| title_fullStr | Resample-smoothing of Voronoi intensity estimators |
| title_full_unstemmed | Resample-smoothing of Voronoi intensity estimators |
| title_short | Resample-smoothing of Voronoi intensity estimators |
| title_sort | resample-smoothing of voronoi intensity estimators |
| url | http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/74457 |