# Nonparametric inference for Poisson-Laguerre tessellations

arXiv: https://arxiv.org/abs/2501.08810 · HTML: https://mlsanity.com/paper/2501.08810/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing](https://mlsanity.com/paper/2507.14268/) (2025)

## Abstract (arXiv)

In this paper, we consider statistical inference for Poisson-Laguerre tessellations in ℝd. 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.