Nonparametric inference for Poisson-Laguerre tessellations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909940690452480 |
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| author | van der Jagt, Thomas Jongbloed, Geurt Vittorietti, Martina |
| author_facet | van der Jagt, Thomas Jongbloed, Geurt Vittorietti, Martina |
| contents | In this paper, we consider statistical inference for Poisson-Laguerre tessellations in $\mathbb{R}^d$. The object of interest is a distribution function $F$ which uniquely determines the intensity measure of the underlying Poisson process. Two nonparametric estimators for $F$ are introduced which depend only on the points of the Poisson process which generate non-empty cells and the actual cells corresponding to these points. The proposed estimators are proven to be strongly consistent, as the observation window expands unboundedly to the whole space. We also consider a stereological setting, where one is interested in estimating the distribution function associated with the Poisson process of a higher dimensional Poisson-Laguerre tessellation, given that a corresponding sectional Poisson-Laguerre tessellation is observed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_08810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric inference for Poisson-Laguerre tessellations van der Jagt, Thomas Jongbloed, Geurt Vittorietti, Martina Statistics Theory Methodology 62G05, 60D05 In this paper, we consider statistical inference for Poisson-Laguerre tessellations in $\mathbb{R}^d$. The object of interest is a distribution function $F$ which uniquely determines the intensity measure of the underlying Poisson process. Two nonparametric estimators for $F$ are introduced which depend only on the points of the Poisson process which generate non-empty cells and the actual cells corresponding to these points. The proposed estimators are proven to be strongly consistent, as the observation window expands unboundedly to the whole space. We also consider a stereological setting, where one is interested in estimating the distribution function associated with the Poisson process of a higher dimensional Poisson-Laguerre tessellation, given that a corresponding sectional Poisson-Laguerre tessellation is observed. |
| title | Nonparametric inference for Poisson-Laguerre tessellations |
| topic | Statistics Theory Methodology 62G05, 60D05 |
| url | https://arxiv.org/abs/2501.08810 |