# Convex and non-convex regularization methods for spatial point processes intensity estimation

## TL;DR

This paper introduces regularization techniques for spatial point process intensity estimation, ensuring consistency and sparsity, with practical implementation and application to forestry data.

## Contribution

It develops new regularized estimation methods for spatial point processes, providing theoretical guarantees and demonstrating their effectiveness through simulations and real data.

## Key findings

- Methods achieve consistency and sparsity.
- Numerical implementation is feasible and effective.
- Application to forestry data demonstrates practical utility.

## Abstract

This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood and logistic regression likelihood. We provide general conditions on the spatial point processes and on penalty functions which ensure consistency, sparsity and asymptotic normality. We discuss the numerical implementation and assess finite sample properties in a simulation study. Finally, an application to tropical forestry datasets illustrates the use of the proposed methods.