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Kernel Estimation of the Spectral Density of Stationary Random Closed Sets

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Summary

A non-parametric kernel estimator of the spectral density of stationary random closed sets is studied. Conditions are derived under which this estimator is asymptotically unbiased and mean-square consistent. For the planar Boolean model with isotropic compact and convex grains, an averaged version of the kernel estimator is compared with the theoretical spectral density.
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Keywords: Boolean model; asymptotic unbiasedness; mean-square consistency; non-parametric kernel estimator; spectral density; stationary random set

Document Type: Research Article

Affiliations: 1: Dept of Stochastics, University of Ulm, Germany 2: Institute of Mathematics, University of Augsburg, Germany

Publication date: March 1, 2004

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