Semiparametric Spatial Point Processes

TL;DR

This paper develops a semiparametric model for spatial point processes with both parametric and nonparametric components, providing efficient estimators and demonstrating their effectiveness through simulations and real data applications.

Contribution

It introduces a novel semiparametric framework for spatial point processes, including efficient estimation methods for both components and computational techniques.

Findings

Estimator achieves semiparametric efficiency lower bound for Poisson patterns.

Estimator is consistent and asymptotically normal for non-Poisson patterns.

Simulation and real data analyses validate the proposed methods.

Abstract

We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric components. For the parametric component, we derive the semiparametric efficiency lower bound under Poisson point patterns and propose a point process double machine learning estimator that can achieve this lower bound. The proposed estimator for the parametric component is also shown to be consistent and asymptotically normal for non-Poisson point patterns. For the nonparametric component, we propose a kernel-based estimator and characterize its rates of convergence. Computationally, we introduce a fast, numerical approximation that transforms the proposed estimator into an estimator derived from weighted generalized partial linear models. We conclude with a simulation study and two real data analyses from ecology and hydrogeology.