Inhomogeneous higher-order summary statistics for linear network point processes

TL;DR

This paper develops new inhomogeneous higher-order summary statistics for linear network point processes, providing geometrically corrected estimators and demonstrating their effectiveness through simulations and real data analysis.

Contribution

It introduces a novel framework for inhomogeneous higher-order summary statistics on linear networks, including new estimators and their application to real-world datasets.

Findings

Proposed geometrically corrected summary statistics perform well in simulations.

The methodology effectively analyzes traffic accident and spider data.

Non-parametric estimators are feasible and useful for spatial interaction analysis.

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.