Statistics for Poisson Models of Overlapping Spheres. (December 2014)

• Record Type: Journal Article
• Authors: Hug, Daniel; Last, Günter; Pawlas, Zbyněk; Weil, Wolfgang
• Is Part Of: Advances in applied probability. Volume 46:Number 4(2014)
• Page Start: 937
• Page End: 962
• Publication Date: 2014-12
• Subjects: Stochastic geometry, -- spatial statistic, -- contact distribution function, -- Boolean model, -- spherical typical grain, -- point process, -- nonparametric estimation, -- radius distribution, -- asymptotic normality; 60D05, -- 60G57, -- 52A21, -- 60G55, -- 52A22, -- 52A20, -- 53C65, -- 46B20, -- 62G05; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/S0001867800007497
• Languages: English
• ISSNs: 0001-8678

Abstract

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.