Variance Estimation for Statistics Computed from Inhomogeneous Spatial Point Processes

This paper introduces a new approach to estimate the variance of statistics that are computed from an inhomogeneous spatial point process. The proposed approach 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 proposed approach is demonstrated in two important applications of modeling inhomogeneous spatial point processes: 1) residual diagnostics of a fitted model, and 2) 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 proposed approach. Yongtao Guan is Assistant Professor, Division of Biostatistics, Yale School of Public Health, Yale University, New Haven, CT 06520.8034, e-mail [email protected]. The author would like to thank Rasmus Waagepetersen for helpful discussions on the Beilschmiedia pendula Lauraceae data, and the Editor, an Associate Editor and two referees for helpful comments that have improved the paper.