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