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Asymptotic properties of estimators for the volume fractions of jointly stationary random sets
Author(s) -
Böhm S.,
Schmidt V.,
Heinrich L.
Publication year - 2004
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2004.00267.x
Subject(s) - estimator , mathematics , covariance , boolean model , covariance matrix , representation (politics) , random matrix , matrix (chemical analysis) , multivariate random variable , discrete mathematics , statistics , random variable , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , politics , political science , law , composite material
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.