Statistical estimation of Poisson intensity functions

This survey paper is concerned with nonparametric estimation of the global and local intensity of a cyclic Poisson point process $X$. We assume that only a single realization of $X$ is observed, though only within a bounded 'window', and our aim is to estimate consistently the global intensity and the intensity function at a given point. A simple nonparametric estimator for the global intensity is proposed and studied. We also give a preview of recent work by the present authors, in part joint with R. Zitikis (Winnipeg), on nonparametric estimation of the local intensity at a given point.