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Journal Articles Annals of Applied Probability Year : 2016

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

Marianne Clausel
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Jean-François Coeurjolly
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 in Rd and observed in a bounded window. The procedure is based on a new general 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 particular, we show that in many practical situations we have a gain larger than 30%.
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Dates and versions

hal-01024648 , version 1 (16-07-2014)
hal-01024648 , version 2 (19-03-2015)
hal-01024648 , version 3 (30-07-2015)

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Marianne Clausel, Jean-François Coeurjolly, Jérôme Lelong. Stein estimation of the intensity of a spatial homogeneous Poisson point process. Annals of Applied Probability, 2016, 26 (3), pp.1495-1534. ⟨10.1214/15-AAP1124⟩. ⟨hal-01024648v3⟩
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