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

• 成果类型: Article
• 署名作者: Barr, C. D.; Schoenberg, F. P.
• 署名单位: Harvard University; University of California System; University of California Los Angeles
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq047
• 发表日期: 2010
• 页码: 977984
• 关键词: point-process models; tessellation

摘要

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