Moment estimation for parametric spatial Cox process models

In the talk we will discuss parameter estimation for homogeneous and inhomogeneous spatial Cox processes. We first give an overview of the moment estimation methods for the homogeneous case and then we discuss parameter estimation for Cox models with inhomogeneity introduced by location dependent thinning. In the first step the inhomogeneity is estimated by means of the Poisson likelihood. Then conditionally on the estimated inhomogeneity parameters the interaction (clustering) parameters are estimated. This was done previously by means of the minimum contrast on the inhomogeneous K-function. We introduce two alternative estimators using composite likelihood and Palm likelihood, compare them with the previous method and discuss their properties.