Asymptotic properties of estimators for the volume fractions of jointly stationary random sets |
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Authors: | S Böhm V Schmidt ‡ L Heinrich † |
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Institution: | Department of Stochastics, University of Ulm, D-89069 Ulm, Germany;, and Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany |
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Abstract: | In the present paper, we show how a consistent estimator can be derived for the asymptotic covariance matrix of stationary 0–1-valued vector fields in R d , whose supports are jointly stationary random closed sets. As an example, which is of particular interest for statistical applications, we consider jointly stationary random closed sets associated with the Boolean model in R d such that the components indicate the frequency of coverage by the single grains of the Boolean model. For this model, a representation formula for the entries of the covariance matrix is obtained. |
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Keywords: | stationary vector field covariance matrix estimation consistency Boolean model frequency of coverage |
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