Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 46, Number 4 (2014), 937-962.
Statistics for Poisson models of overlapping spheres
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.
Adv. in Appl. Probab., Volume 46, Number 4 (2014), 937-962.
First available in Project Euclid: 12 December 2014
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Mathematical Reviews number (MathSciNet)
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Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60G57: Random measures 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
Secondary: 60G55: Point processes 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx] 46B20: Geometry and structure of normed linear spaces 62G05: Estimation
Hug, Daniel; Last, Günter; Pawlas, Zbynȫk; Weil, Wolfgang. Statistics for Poisson models of overlapping spheres. Adv. in Appl. Probab. 46 (2014), no. 4, 937--962. doi:10.1239/aap/1418396238. https://projecteuclid.org/euclid.aap/1418396238