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 kernel-smoothing 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 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 theuse of the proposed procedures.