The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 3 (2016), 1495-1534.
Stein estimation of the intensity of a spatial homogeneous Poisson point process
Marianne Clausel, Jean-François Coeurjolly, and Jérôme Lelong
Abstract
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 $\mathbb{R}^{d}$ 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%.
Article information
Source
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1495-1534.
Dates
Received: July 2014
Revised: March 2015
First available in Project Euclid: 14 June 2016
Permanent link to this document
https://projecteuclid.org/euclid.aoap/1465905010
Digital Object Identifier
doi:10.1214/15-AAP1124
Mathematical Reviews number (MathSciNet)
MR3513597
Zentralblatt MATH identifier
1345.60045
Subjects
Primary: 60G55: Point processes
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Keywords
Stein formula Malliavin calculus superefficient estimator intensity estimation spatial point process
Citation
Clausel, Marianne; Coeurjolly, Jean-François; Lelong, Jérôme. Stein estimation of the intensity of a spatial homogeneous Poisson point process. Ann. Appl. Probab. 26 (2016), no. 3, 1495--1534. doi:10.1214/15-AAP1124. https://projecteuclid.org/euclid.aoap/1465905010