Nonparametric estimation of interaction functions for two-type pairwise interaction point processes

Nonparametric estimation of interaction functions for two-type pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point process converge to the means of an inhomogeneous Poisson process. This suggests a simple and effective nonparametric estimation method. An example is presented to illustrate the efficacy of our method. Our results can be generalized to multitype point processes in a straightforward manner, although the notation is more involved