A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns

When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say β̂, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of β̂ except in some special cases. In this article we show that β̂ is asymptotically normal for a general class of mixing processes. To estimate the variance of β̂, we propose a novel thinned block bootstrap procedure that assumes that the point process is second-order reweighted stationary. To apply this procedure, only the FOIF, and not any high-order terms of the process, needs to be estimated. We establish the consistency of the resulting variance estimator, and demonstrate its efficacy through simulations and an application to a real data example.