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 β, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of β except in some special cases. In this article we show that β is asymptotically normal for a general class of mixing processes. To estimate the variance of β, 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.