Inhomogeneous higher-order summary statistics for linear network point processes

Abstract

We introduce the notion of intensity reweighted moment pseudostationary point processes on linear networks. Based on arbitrary general regular linear network distances, we propose geometrically corrected versions of different higher-order summary statistics, including the inhomogeneous empty space function, the inhomogeneous nearest neighbour distance distribution function and the inhomogeneous $J$-function. We also discuss their non-parametric estimators. Through a simulation study, considering models with different types of spatial interaction, we study the performance of our proposed summary statistics. Finally, we make use of our methodology to analyse two datasets: motor vehicle traffic accidents and spider data.