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Nonparametric estimation of the chord length distribution

Part of: Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Martin B. Hansen  and
Erik W. van Zwet
Martin B. Hansen*
Affiliation:
Aalborg University
Erik W. van Zwet*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg Ø, Denmark. Email address: mbh@math.auc.dk
∗∗ Postal address: University of California, Department of Statistics, 367 Evans Hall #3860, Berkeley, CA 94720-3860, USA.
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Abstract

The distribution of the length of a typical chord of a stationary random set is an interesting feature of the set's whole distribution. We give a nonparametric estimator of the chord length distribution and prove its strong consistency. We report on a simulation experiment in which our estimator compared favourably to a reduced sample estimator. Both estimators are illustrated by applying them to an image sample from a yoghurt ferment. We briefly discuss the closely related problem of estimation of the linear contact distribution. We show by a simulation experiment that a transformation of our estimator of the chord length distribution is more efficient than a Kaplan-Meier type estimator of the linear contact distribution.

Keywords

Chord length distributionlinear contact distributionnonparametric maximum likelihood estimationmissing data

MSC classification

Primary: 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 3 , September 2001 , pp. 541 - 558
Copyright
Copyright © Applied Probability Trust 2001 

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