## The Annals of Applied Probability

### Stein estimation of the intensity of a spatial homogeneous Poisson point process

#### 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
Revised: March 2015
First available in Project Euclid: 14 June 2016

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

#### 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

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