Statistics for Poisson models of overlapping spheres
Probability
2013-01-09 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1301.1499,
title = {Statistics for Poisson models of overlapping spheres},
author = {Daniel Hug and Günter Last and Zbyněk Pawlas and Wolfgang Weil},
journal= {arXiv preprint arXiv:1301.1499},
year = {2013}
}