Adaptive density estimation in the pile-up model involving measurement errors

Motivated by fluorescence lifetime measurements, this paper considers the problem of nonparametric density estimation in the pile-up model, where observations suffer also from measurement errors. In the pile-up model, an observation is defined as the minimum of a random number of i.i.d. variables following the target distribution. Adaptive nonparametric estimators are proposed for this pile-up model with measurement errors. Furthermore, oracle type risk bounds for the mean integrated squared error (MISE) are provided. Finally, the estimation method is assessed by a simulation study and the application to real fluorescence lifetime data.