Infill asymptotics for logistic regression estimators for spatio-temporal point processes

TL;DR

This paper investigates the asymptotic properties of logistic regression estimators in spatio-temporal point processes with log-linear intensities, establishing consistency, normality, and extensions to general models and estimating equations.

Contribution

It provides new theoretical results on the asymptotic behavior of estimators for spatio-temporal point processes, including extensions to broader models and estimation methods.

Findings

Proves strong consistency of estimators

Establishes asymptotic normality under infill asymptotics

Extends results to general point process models and unbiased estimating equations

Abstract

This paper discusses infill asymptotics for logistic regression estimators for spatio-temporal point processes whose intensity functions are of log-linear form. We establish strong consistency and asymptotic normality for the parameters of a Poisson point process model and demonstrate how these results can be extended to general point process models. Additionally, under proper conditions, we also extend our central limit theorem to other unbiased estimating equations that are based on the Campbell--Mecke theorem.