Nonparametric intensity estimation of spatial point processes by random forests

TL;DR

This paper introduces a novel random forest-based method for estimating the intensity of spatial point processes, effectively handling covariates, irregular domains, and providing theoretical guarantees.

Contribution

It develops a nonparametric intensity estimator using random forests that is flexible, consistent, and adaptable to complex spatial domains, with theoretical and empirical validation.

Findings

Performs competitively with existing methods

Handles large covariate sets and irregular domains

Provides consistency and convergence guarantees

Abstract

We propose a random forest estimator for the intensity of spatial point processes, applicable with or without covariates. It retains the well-known advantages of a random forest approach, including the ability to handle a large number of covariates, out-of-bag cross-validation, and variable importance assessment. Importantly, even in the absence of covariates, it requires no border correction and adapts naturally to irregularly shaped domains and manifolds. Consistency and convergence rates are established under various asymptotic regimes, revealing the benefit of using covariates when available. Numerical experiments illustrate the methodology and demonstrate that it performs competitively with state-of-the-art methods.