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

Fabienne Comte (1) , Tabea Rebafka (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Fabienne Comte, Tabea Rebafka. Adaptive Density Estimation in the Pile-up Model Involving Measurement Errors. Electronic Journal of Statistics , 2012, 6, pp.2002-2037. ⟨10.1214/12-EJS737⟩. ⟨hal-00531272⟩