On the Voronoi estimator for the intensity of an inhomogeneous planar Poisson process

摘要

The Voronoi estimator may be defined for any location as the inverse of the area of the correspondingnVoronoi cell. We investigate the statistical properties of this estimator for the intensity of an inhomoge-nneous Poisson process, and demonstrate it is approximately unbiased with a gamma sampling distribution.nWe also introduce the centroidal Voronoi estimator, a simple extension based on spatial regularizationnof the point pattern. Simulations show the Voronoi estimator has remarkably low bias, while the cen-ntroidal Voronoi estimator has slightly more bias but is much less variable. The performance is comparednto kernel estimators using two simulated datasets and a dataset consisting of earthquakes within thencontinental United States.