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Asymptotic properties of estimators for parameters of the Boolean model

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

Published online by Cambridge University Press:  01 July 2016

Ilya Molchanov  and
Dietrich Stoyan
Ilya Molchanov*
Affiliation:
Freiberg University of Mining and Technology
Dietrich Stoyan*
Affiliation:
Freiberg University of Mining and Technology
*
* On leave from Kiev Technological Institute of the Food Industry.
** Postal address: TU Bergakademie Freiberg, Institut für Stochastik, D-09596 Freiberg, Germany.
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Abstract

This paper considers estimators of parameters of the Boolean model which are obtained by means of the method of intensities. For an estimator of the intensity of the point process of germ points the asymptotic normality is proved and the corresponding variance is given. The theory is based on a study of second-order characteristics of the point process of lower-positive tangent points of the Boolean model. An estimator of the distribution of a typical grain is also discussed.

Keywords

ASYMPTOTIC NORMALITYINTENSITYPOINT PROCESSRANDOM SETPARTICLE SYSTEM

MSC classification

Primary: 62M30: Spatial processes
Secondary: 60D05: Geometric probability and stochastic geometry 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 301 - 323
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

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

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