Non-parametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets

TL;DR

This paper introduces new non-parametric summary statistics to measure dependence between components in inhomogeneous multivariate random measures and sets, extending classical methods for stationary models.

Contribution

It develops coverage-reweighted cumulant density-based statistics for inhomogeneous models, with explicit relations, unbiased estimators, and applications to simulated data.

Findings

New dependence measures for multivariate random measures.

Explicit formulas and unbiased estimators provided.

Validated through simulated examples.

Abstract

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.