Asymptotic properties of estimators for the volume fractions of jointly stationary random sets

S. Böhm, V. Schmidt and L. Heinrich

Statistica Neerlandica, 2004, vol. 58, issue 4, 388-406

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 ℝd, 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 ℝd 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.

Date: 2004
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