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Surprising optimal estimators for the area fraction

Part of: Stochastic processes Geometric probability and stochastic geometry Design of experiments

Published online by Cambridge University Press:  01 July 2016

Katja Schladitz
Katja Schladitz*
Affiliation:
Aalborg University
*
∗ Postal address: Department of Mathematics, Aalborg University, Fredrik Bajers Vej 7E, 9220 Aalborg, Denmark. Email address: katja@math.auc.dk
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Abstract

For a random closed set X and a compact observation window W the mean coverage fraction of W can be estimated by measuring the area of W covered by X. Jensen and Gundersen, and Baddeley and Cruz-Orive described cases where a point counting estimator is more efficient than area measurement. We give two other examples, where at first glance unnatural estimators are not only better than the area measurement but by Grenander's Theorem have minimal variance. Whittle's Theorem is used to show that the point counting estimator in the original Jensen-Gundersen paradox is optimal for large randomly translated discs.

Keywords

Random closed setarea fractioncoverage fractionunbiased estimatorminimum varianceJensen-Gundersen paradoxGrenander's theoremWhittle's theoremsampling designoptimal design

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60G55: Point processes
Secondary: 62K05: Optimal designs
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 4 , December 1999 , pp. 995 - 1001
Copyright
Copyright © Applied Probability Trust 1999 

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References

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