Non-parametric indices of dependence between types for inhomogeneous multivariate random closed sets.

Abstract

We propose new summary statistics to quantify the correlation between \nthe components in coverage-reweighted moment stationary multivariate \nrandom closed sets. They are defined in terms of the coverage-reweighted \ncumulant densities and under stationarity reduce to the reduced cross \ncorrelation measure and cross hitting functional proposed by Stoyan \nand Ohser (1982). Unbiased estimators are given for all statistics \nand applied to simulations of a bivariate germ-grain model. \