Spatial point processes intensity estimation with a diverging number of covariates

TL;DR

This paper develops a method for estimating the intensity of spatial point processes with a diverging number of covariates, ensuring statistical properties like consistency and sparsity, supported by simulations and real data application.

Contribution

It introduces a novel estimation framework for high-dimensional covariates in spatial point processes, extending existing methods to diverging covariate scenarios.

Findings

Establishes consistency, sparsity, and asymptotic normality under certain conditions.

Validates theoretical results through simulations.

Demonstrates applicability with forestry dataset analysis.

Abstract

Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the number of covariates diverges as the domain of observation increases. In particular, we consider estimating equations based on Campbell theorems derived from Poisson and logistic regression likelihoods regularized by a general penalty function. We prove that, under some conditions, the consistency, the sparsity, and the asymptotic normality are valid for such a setting. We support the theoretical results by numerical ones obtained from simulation experiments and an application to forestry datasets.