Infill asymptotics for logistic regression estimators for parameters of the intensity function of spatial point processes

This paper discusses infill asymptotics for logistic regression estimators for spatial point processes whose intensity functions are of log-linear form. First, we establish strong consistency and asymptotic normality for the parameters of a Poisson point process model. We also propose consistent estimators for the asymptotic covariance matrix. Next, we extend the results to general point process models for which replicated realizations are available and, under proper conditions, extend the central limit theorem to estimators from other unbiased estimating equations that are based on the Campbell–Mecke theorem. In a simulation study, we demonstrate the efficiency of a regular dummy point process in logistic regression estimation and pseudo-likelihood estimation. Finally, we demonstrate the approach on data on kitchen fires in the Twente region in the Netherlands.