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Statistics of the Boolean model: from the estimation of means to the estimation of distributions

Part of: Stochastic processes Geometric probability and stochastic geometry Limit theorems Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Ilya S. Molchanov
Ilya S. Molchanov*
Affiliation:
Freiberg University of Mining and Technology
*
* Present address: CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.
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Abstract

Non-parametric estimators of the distribution of the grain of the Boolean model are considered. The technique is based on the study of point processes of tangent points in different directions related to the Boolean model. Their second- and higher-order characteristics are used to estimate the mean body and the distribution of the typical grain. Central limit theorems for the improved estimator of the intensity and surface measures of the Boolean model are also proved.

Keywords

DEPENDENT THINNINGINTENSITYPOISSON PROCESSRANDOM CLOSED SETSURFACE MEASURE

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 62M30: Spatial processes 60F05: Central limit and other weak theorems
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 63 - 86
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This work was supported by the Alexander von Humboldt-Stiftung, Bonn, Germany.

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain on 21–24 September 1993.

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