Laguerre basis for inverse problems

Abstract : We present a series of inverse problems of nonparametric statistics which have an easy solution using projection estimators on a Laguerre basis. The models are Yi = XiUi, Zi = Xi +Vi, Wi = (Xi +Vi)Ui, Ti = XiUi +Vi, i = 1,. .. , n where the Xi's and Vi's are nonnegative, the Xi's are i.i.d. with unknown density f , the Vi's are i.i.d. with known density fV , the Ui's are i.i.d. with uniform density on [0, 1]. The sequences (Xi), (Ui), (Vi) are independent. We aim at estimating f on R + in the four cases of indirect observations of (X1,. .. , Xn). We propose projection estimators using a Laguerre basis and give upper bounds of their L 2-risks on specific Sobolev-Laguerre spaces. In each case, a data-driven procedure is described and proved to perform automatically the bias variance compromise. (1) Université Paris Descartes, MAP5, UMR CNRS 8145,
Type de document :
Pré-publication, Document de travail
MAP5 2017-05. 2017
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01449799
Contributeur : Fabienne Comte <>
Soumis le : lundi 30 janvier 2017 - 16:57:39
Dernière modification le : jeudi 2 février 2017 - 01:04:52

Fichier

LaguerreInverse1.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01449799, version 1

Collections

Citation

Fabienne Comte, Valentine Genon-Catalot. Laguerre basis for inverse problems . MAP5 2017-05. 2017. <hal-01449799>

Partager

Métriques

Consultations de
la notice

72

Téléchargements du document

30