Abstract
In this paper we consider the stationary Poisson Boolean model with spherical grains and propose 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 a growing observation window. We show 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. We also provide a short discussion of related estimators as well as a simulation study.
Citation
Daniel Hug. Günter Last. Zbynȫk Pawlas. Wolfgang Weil. "Statistics for Poisson models of overlapping spheres." Adv. in Appl. Probab. 46 (4) 937 - 962, December 2014. https://doi.org/10.1239/aap/1418396238
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