Variance estimation for statistics computed from inhomogeneous spatial point processes

Abstract

The paper introduces a new approach to estimate the variance of statistics that are computed from an inhomogeneous spatial point process. The approach proposed is based on the assumption that the observed point process can be thinned to be a second-order stationary point process, where the thinning probability depends only on the first-order intensity function of the (unthinned) original process. The resulting variance estimator is proved to be asymptotically consistent for the target parameter under some very mild conditions. The use of the approach proposed is demonstrated in two important applications of modelling inhomogeneous spatial point processes: residual diagnostics of a fitted model and inference on the unknown regression coefficients. A simulation study and an application to a real data example are used to demonstrate the efficacy of the approach proposed. © 2008 Royal Statistical Society.