Motivated by fluorescence lifetime measurements this paper considers the
problem of nonparametric density estimation in the pile-up model. Adaptive
nonparametric estimators are proposed for the pile-up model in its simple form
as well as in the case of additional measurement errors. Furthermore, oracle
type risk bounds for the mean integrated squared error (MISE) are provided.
Finally, the estimation methods are assessed by a simulation study and the
application to real fluorescence lifetime data.