Variance estimation for statistics computed from inhomogeneous spatial point processes

Author: Guan, Yongtao¹

Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 70, Number 1, February 2008 , pp. 175-190(16)

Publisher: Blackwell Publishing

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Abstract:

Summary.

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.

Keywords: Inhomogeneous spatial point process; Second-order reweighted stationarity; Thinning

Document Type: Research article

DOI: 10.1111/j.1467-9868.2007.00632.x

Affiliations: 1: Yale University, New Haven, USA

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