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Estimation variances for Poisson processes of compact sets

Part of: Sufficiency and information Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Tomáš Mrkvička
Tomáš Mrkvička*
Affiliation:
Charles University, Prague
*
∗ Postal address: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675, Praha 8, Czech Republic. Email address: mrkvicka@karlin.mff.cuni.cz
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Abstract

A complete and sufficient statistic is found for various stationary Poisson processes of compact sets with known primary grain. In the particular case of a segment process, the uniformly best unbiased estimator for the length density is the number of segments hitting the sampling window divided by a certain constant and multiplied by the mean segment length.

Keywords

Complete statisticintensity estimationPoisson processRao-Blackwell theoremsegment processsufficient statisticBoolean model

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 62B05: Sufficient statistics and fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 4 , December 2001 , pp. 765 - 772
Copyright
Copyright © Applied Probability Trust 2001 

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