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Asymptotic properties of stereological estimators of volume fraction for stationary random sets

Published online by Cambridge University Press:  14 July 2016

Shigeru Mase
Shigeru Mase*
Affiliation:
Hiroshima University
*
∗Postal address: Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Sende-Machi, 1–1–89, Naka-Ku, Hiroshima, 730 Japan.
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Abstract

We shall discuss asymptotic properties of stereological estimators of volume (area) fraction for stationary random sets (in the sense of Matheron) under natural and general assumptions. Results obtained are strong consistency, asymptotic normality, and asymptotic unbiasedness and consistency of asymptotic variance estimators. The method is analogous to the non-parametric estimation of spectral density functions of stationary time series using window functions. Proofs are given for areal estimators, but they are also valid for lineal and point estimators with slight modifications. Finally we show that stationary Boolean models satisfy the relevant assumptions reasonably well.

Keywords

STEREOLOGYVOLUME FRACTIONRANDOM SETWINDOW FUNCTIONASYMPTOTIC THEORYSTATIONARITYBOOLEAN MODEL
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 111 - 126
Copyright
Copyright © Applied Probability Trust 1982 

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