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Kernel Estimation of the Spectral Density of Stationary Random Closed Sets
Author(s) -
Böhm Stephan,
Heinrich Lothar,
Schmidt Volker
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00310.x
Subject(s) - mathematics , estimator , kernel density estimation , kernel (algebra) , variable kernel density estimation , multivariate kernel density estimation , regular polygon , statistics , kernel method , combinatorics , geometry , artificial intelligence , computer science , support vector machine
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.