We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and extend classic functional statistics for stationary random closed sets. We study the relations between these statistics and evaluate them explicitly for a range of models. Unbiased estimators are given for all statistics and applied to simulated examples and to tropical rain forest data.

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Keywords Bivariate random measure, Coverage-reweighted moment stationarity, Cross hitting functional, Empty space function, J-function, K-function, Moment measure, Reduced cross correlation measure, Spherical contact distribution
Persistent URL dx.doi.org/10.1111/sjos.12331
Journal Scandinavian Journal of Statistics
van Lieshout, M.N.M. (2018). Non-parametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets. Scandinavian Journal of Statistics, 45(4), 985–1015. doi:10.1111/sjos.12331