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Non-parametric estimation of the directional distribution of stationary line and fibre processes

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

Published online by Cambridge University Press:  01 July 2016

Markus Kiderlen
Markus Kiderlen*
Affiliation:
Universität Karlsruhe
*
∗ Postal address: Universität Karlsruhe, Mathematisches Institut II, D-76128 Karlsruhe, Germany. Email address: kiderlen@math.uni-karlsruhe.de
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Abstract

Two non-parametric methods for the estimation of the directional measure of stationary line and fibre processes in d-dimensional space are presented. The input data for both methods are intersection counts with finitely many test windows situated in hyperplanes. The first estimator is a measure valued maximum likelihood estimator, if applied to Poisson line processes. The second estimator uses an approximation of the associated zonoid (the Steiner compact) by zonotopes. Consistency of both estimators is proved (without use of the Poisson assumption). The estimation methods are compared empirically by simulation.

Keywords

rose of directionsplanar sectionfibre processSteiner compactzonoidestimationmaximum likelihood

MSC classification

Primary: 62M30: Spatial processes
Secondary: 62G05: Estimation 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 1 , March 2001 , pp. 6 - 24
Copyright
Copyright © Applied Probability Trust 2001 

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