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

Christopher D. Barr, & Frederic P. Schoenberg

Published December 9, 2010, SCEC Contribution #1286

We investigate the statistical properties of the Voronoi estimator for the intensity of an inhomogeneous Poisson process. The Voronoi estimator may be defined for any location as the inverse of the area of the corresponding Voronoi cell. The estimator is well-known to be unbiased in the case of estimating the intensity of a homogeneous Poisson process, and is shown here to be approximately ratio unbiased in the inhomogeneous case. Simulation studies show the sampling distribution is well approximated by the inverse gamma model, extending similar results from the homogeneous case. Performance of the Voronoi estimator is compared to a kernel estimator using two simulated data sets as well as a dataset consisting of earthquakes within the continental United States.

Citation
Barr, C. D., & Schoenberg, F. P. (2010). On the Voronoi estimator for the intensity of an inhomogeneous planar Poisson process. Biometrika, 97(4), 977-984. doi: 10.1093/biomet/asq047.