  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 $\R^d$ 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\%.
