Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

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

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

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

Kiderlen, M. (2008). Estimation of the mean normal measure from flat sections. *Advances in Applied Probability*, *40*(1), 31-48. https://doi.org/10.1239/aap/1208358885

Kiderlen M. 2008. Estimation of the mean normal measure from flat sections. Advances in Applied Probability. 40(1):31-48. https://doi.org/10.1239/aap/1208358885

Kiderlen, Markus. "Estimation of the mean normal measure from flat sections". *Advances in Applied Probability*. 2008, 40(1). 31-48. https://doi.org/10.1239/aap/1208358885

Kiderlen M. Estimation of the mean normal measure from flat sections. Advances in Applied Probability. 2008;40(1):31-48. https://doi.org/10.1239/aap/1208358885

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

@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",

}

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 -