STEIN ESTIMATION OF THE INTENSITY OF A SPATIAL HOMOGENEOUS POISSON POINT PROCESS

• 成果类型: Article
• 署名作者: Clausel, Marianne; Coeurjolly, Jean-Francois; Lelong, Jerome
• 署名单位: Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1124
• 发表日期: 2016
• 页码: 1495-1534
• 关键词: configuration-spaces; stochastic-analysis; calculus; geometry; drift

摘要

In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined on R-d and observed on a bounded window. The procedure is based on a new integration by parts formula for Poisson point processes. We show that our Stein estimator outperforms the maximum likelihood estimator in terms of mean squared error. In many practical situations, we obtain a gain larger than 30%.