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Unbiased stereological estimation of the surface area of gradient surface processes

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

Published online by Cambridge University Press:  01 July 2016

Ute Hahn  and
Dietrich Stoyan
Ute Hahn*
Affiliation:
University of Western Australia
Dietrich Stoyan*
Affiliation:
Freiberg University of Mining and Technology
*
∗ Postal address: Department of Mathematics, The University of Western Australia, Nedlands, Perth, WA 6907, Australia. Email address: [email protected]
∗∗ Postal address: Institute of Stochastics, Freiberg University of Mining and Technology, 09596 Freiberg, Germany.
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Abstract

An unbiased stereological estimator for surface area density is derived for gradient surface processes which form a particular class of non-stationary spatial surface processes. Vertical planar sections are used for the estimation. The variance of the estimator is studied and found to be infinite for certain types of surface processes. A modification of the estimator is presented which exhibits finite variance.

Keywords

Gradient surface processstereologysurface area densityvertical sections

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 904 - 920
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Dedicated to Professor Mecke on his 60th birthday.

References

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