Substationarity in Spatial Point Processes

TL;DR

This paper introduces the novel concept of substationarity in spatial point processes, proposing a semiparametric estimation approach and demonstrating its effectiveness through simulations and a wildfire data application.

Contribution

It formally defines substationarity, develops estimation methods for the linear subspace and intensity function, and applies these to real wildfire data to reveal spatial invariance.

Findings

Estimators of substationarity are reliable in simulations.

Wildfire occurrences show substationarity along longitude.

Latitude is more influential than longitude in wildfire patterns.

Abstract

The goal of the article is to develop the approach of substationarity to spatial point processes (SPPs). Substationarity is a new concept, which has never been studied in the literature. It means that the distribution of SPPs can only be invariant under location shifts within a linear subspace of the domain. Theoretically, substationarity is a concept between stationariy and nonstationarity, but it belongs to nonstationarity. To formally propose the approach, the article provides the definition of substationarity and an estimation method for the first-order intensity function. As the linear subspace may be unknown, it recommends using a parametric way to estimate the linear subspace and a nonparametric way to estimate the first-order intensity function, indicating that it is a semiparametric approach. The simulation studies show that both the estimators of the linear subspace and the first-order intensity function are reliable. In an application to a forest wildfire data set, the article concludes that substationarity of wildfire occurrences may be assumed along the longitude, indicating that latitude is a more important factor than longitude in forest wildfire studies.