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Kernel Estimation of the Spectral Density of Stationary Random Closed Sets |
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| Authors: | Stephan Bö hm,Lothar Heinrich,Volker Schmidt |
| Affiliation: | Dept of Stochastics, University of Ulm, Germany;Institute of Mathematics, University of Augsburg, Germany |
| Abstract: | 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. |
| Keywords: | asymptotic unbiasedness mean-square consistency non-parametric kernel estimator spectral density Boolean model stationary random set |