Adaptive Density Estimation in the Pile-up Model Involving Measurement Errors

TL;DR

This paper develops adaptive nonparametric density estimators for the pile-up model with measurement errors, providing theoretical risk bounds and demonstrating effectiveness through simulations and real data application.

Contribution

It introduces new adaptive estimators for the pile-up model with measurement errors and derives oracle risk bounds, advancing nonparametric density estimation methods.

Findings

Estimators achieve near-optimal risk bounds.

Simulation results confirm estimator performance.

Application to fluorescence data demonstrates practical utility.

Abstract

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.