Statistics for Poisson models of overlapping spheres

2013/01/08 by Daniel Hug, Hug, Daniel, Günter Last +5
Economics, Econometrics and Finance · Environmental Science · Mathematics · #46B20 #52A20 #52A21 #52A22 #53C65 #60D05 #60G55 #60G57 #62G05 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1301.1499

openalex publication_date 2013/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an appropriate way. They are ratio-unbiased and asymptotically consistent for growing observation window. It is shown that the asymptotic variance exists and is given by a fairly explicit integral expression. Asymptotic normality is established under a suitable integrability assumption on the weight function. The paper also provides a short discussion of related estimators as well as a simulation study.

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