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June 2016 Stein estimation of the intensity of a spatial homogeneous Poisson point process
Marianne Clausel, Jean-François Coeurjolly, Jérôme Lelong
Ann. Appl. Probab. 26(3): 1495-1534 (June 2016). DOI: 10.1214/15-AAP1124

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%.

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Marianne Clausel. Jean-François Coeurjolly. Jérôme Lelong. "Stein estimation of the intensity of a spatial homogeneous Poisson point process." Ann. Appl. Probab. 26 (3) 1495 - 1534, June 2016. https://doi.org/10.1214/15-AAP1124

Information

Received: 1 July 2014; Revised: 1 March 2015; Published: June 2016
First available in Project Euclid: 14 June 2016

zbMATH: 1345.60045
MathSciNet: MR3513597
Digital Object Identifier: 10.1214/15-AAP1124

Subjects:
Primary: 60G55
Secondary: 60H07

Keywords: intensity estimation , Malliavin calculus , spatial point process , Stein formula , superefficient estimator

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 3 • June 2016
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