  We focus on the estimation of the intensity of a Poisson process in the
presence of a uniform noise. We propose a kernel-based procedure fully
calibrated in theory and practice. We show that our adaptive estimator is
optimal from the oracle and minimax points of view, and provide new lower
bounds when the intensity belongs to a Sobolev ball. By developing the
Goldenshluger-Lepski methodology in the case of deconvolution for Poisson
processes, we propose an optimal data-driven selection of the kernel bandwidth.
Our method is illustrated on the spatial distribution of replication origins
and sequence motifs along the human genome.
