2025/01/15 by Thomas van der Jagt, Geurt Jongbloed, van der Jagt, Thomas +3
Computer Science · Environmental Science · #60D05 #62G05 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Soil Geostatistics and Mapping #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2501.08810
openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.