Nonparametric Estimation in a Multiplicative Censoring Model with Symmetric Noise

Abstract : We consider the model Yi = XiUi, i =1,. .. , n, where the Xi, the Ui and thus the Yi are all independent and identically distributed. The Xi have density f and are the variables of interest, the Ui are multiplicative noise with uniform density on [1-a, 1+a], for some 0 < a < 1, and the two sequences are independent. However, only the Yi are observed. We study nonparametric estimation of both the density f and the corresponding survival function. In each context, a projection estimator of an auxiliary function is built, from which estimator of the function of interest is deduced. Risk bounds in term of integrated squared error are provided, showing that the dimension parameter associated with the projection step has to perform a compromise. Thus, a model selection strategy is proposed in both cases of density and survival function estimation. The resulting estimators are proven to reach the best possible risk bounds. Simulation experiments illustrate the good performances of the estimators and a real data example is described.
Type de document :
Article dans une revue
Journal of Nonparametric Statistics, American Statistical Association, 2016, 28 (4), pp.768-801. <10.1080/10485252.2016.1225737>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01252780
Contributeur : Charlotte Dion <>
Soumis le : vendredi 8 janvier 2016 - 11:18:03
Dernière modification le : vendredi 21 octobre 2016 - 11:19:37

Fichier

mult_censoring_07012016.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Fabienne Comte, Charlotte Dion. Nonparametric Estimation in a Multiplicative Censoring Model with Symmetric Noise. Journal of Nonparametric Statistics, American Statistical Association, 2016, 28 (4), pp.768-801. <10.1080/10485252.2016.1225737>. <hal-01252780>

Partager

Métriques

Consultations de
la notice

196

Téléchargements du document

65