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Markus Kiderlen

Estimation of the mean normal measure from flat sections

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Estimation of the mean normal measure from flat sections. / Kiderlen, Markus.

In: Advances in Applied Probability, Vol. 40, No. 1, 2008, p. 31-48.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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Kiderlen, M 2008, 'Estimation of the mean normal measure from flat sections', Advances in Applied Probability, vol. 40, no. 1, pp. 31-48. https://doi.org/10.1239/aap/1208358885

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Kiderlen, Markus. / Estimation of the mean normal measure from flat sections. In: Advances in Applied Probability. 2008 ; Vol. 40, No. 1. pp. 31-48.

Bibtex

@article{a31d53c070d711dcbee902004c4f4f50,
title = "Estimation of the mean normal measure from flat sections",
abstract = "We discuss the determination of the mean normal measure of a stationary random set Z in the extended convex ring in d-dimensional space by measurements taken in intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z, if k>2 or k=2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified by mean normal measures of intersections with almost all m-tuples of planes, when m> [d/k]. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.",
keywords = "mean normal measure, stereology, Crofton formula",
author = "Markus Kiderlen",
year = "2008",
doi = "10.1239/aap/1208358885",
language = "English",
volume = "40",
pages = "31--48",
journal = "Advances in Applied Probability",
issn = "0001-8678",
publisher = "Applied Probability Trust",
number = "1",

}

RIS

TY - JOUR

T1 - Estimation of the mean normal measure from flat sections

AU - Kiderlen, Markus

PY - 2008

Y1 - 2008

N2 - We discuss the determination of the mean normal measure of a stationary random set Z in the extended convex ring in d-dimensional space by measurements taken in intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z, if k>2 or k=2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified by mean normal measures of intersections with almost all m-tuples of planes, when m> [d/k]. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

AB - We discuss the determination of the mean normal measure of a stationary random set Z in the extended convex ring in d-dimensional space by measurements taken in intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z, if k>2 or k=2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified by mean normal measures of intersections with almost all m-tuples of planes, when m> [d/k]. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

KW - mean normal measure

KW - stereology

KW - Crofton formula

U2 - 10.1239/aap/1208358885

DO - 10.1239/aap/1208358885

M3 - Journal article

VL - 40

SP - 31

EP - 48

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 1

ER -