  Voronoi intensity estimators, which are non-parametric estimators for
intensity functions of point processes, are both parameter-free and adaptive;
the intensity estimate at a given location is given by the reciprocal size of
the Voronoi/Dirichlet cell containing that location. Their major drawback,
however, is that they tend to under-smooth the data in regions where the point
density of the observed point pattern is high and over-smooth in regions where
the point density is low. To remedy this problem, i.e. to find some
middle-ground between over- and under-smoothing, we propose an additional
smoothing technique for Voronoi intensity estimators for point processes in
arbitrary metric spaces, which is based on repeated independent thinnings of
the point process/pattern. Through a simulation study we show that our
resample-smoothing technique improves the estimation significantly. In
addition, we study statistical properties such as unbiasedness and variance,
and propose a rule-of-thumb and a data-driven cross-validation approach to
choose the amount of thinning/smoothing to apply. We finally apply our proposed
intensity estimation scheme to two datasets: locations of pine saplings (planar
point pattern) and motor vehicle traffic accidents (linear network point
pattern).
