Non parametric inference for pile-up correction in nuclear spectrometry

We consider the problem of estimating the density f of independent identically distributed couples {(X-k, Y-k)}(k) which are the marks of an homogenous Poisson process, from samples {X-k', Y-k')}(k) deduced from {(X-k, Y-k)}(k) by a non-linear relation coming from the so-called Type II Counter Problem. From a relation between the probability density functions of the sequences, we propose an estimator of the pdf of Y, since common plug-in estimates are suboptimal.