Nonparametric and Parametric Estimation of the Second-Order Structure of Inhomogeneous Spatial Point Processes Using Case-Control Data

We introduce two novel approaches to estimate the pair correlation function, an important second-order property of an inhomogeneous spatial point process, using case-control data. The first approach is based on nonparametric kernelsmoothing while the second approach uses a conditional likelihood to fit a parametric model for the pair correlation function. A great advantage of the proposed methods over other available methods is that they do not require the Yongtao Guan is Assistant Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034, e-mail [email protected]. Rasmus Waagepetersen is Associate Professor, Department of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7G, DK-9220 Aalborg, e-mail [email protected]. Colin Beale is Spatial Ecologist, The Macaulay Institute, Craigiebuckler, Aberdeen AB15 8QH, UK, e-mail [email protected]. Yongtao Guan’s research was partially supported by NSF grant DMS-0706806. 1 often difficult estimation of the intensity of the control process. We establish the consistency of the resulting estimators and discuss how they can be applied for model diagnostics and inference on regression parameters of the case process. Simulations and applications to two real data examples are used to demonstrate the use of the proposed procedures.