December 2014 Statistics for Poisson models of overlapping spheres
Daniel Hug, Günter Last, Zbynȫk Pawlas, Wolfgang Weil
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Adv. in Appl. Probab. 46(4): 937-962 (December 2014). DOI: 10.1239/aap/1418396238

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.

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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

Information

Published: December 2014
First available in Project Euclid: 12 December 2014

zbMATH: 1319.60014
MathSciNet: MR3290424
Digital Object Identifier: 10.1239/aap/1418396238

Subjects:
Primary: 52A21 , 60D05 , 60G57
Secondary: 46B20 , 52A20 , 52A22 , 53C65 , 60G55 , 62G05

Keywords: asymptotic normality , Boolean model , contact distribution function , nonparametric estimation , point process , radius distribution , spatial statistic , spherical typical grain , Stochastic geometry

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 4 • December 2014
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