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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,
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Contributor : Fabienne Comte <>
Submitted on : Monday, January 30, 2017 - 4:57:39 PM
Last modification on : Tuesday, March 24, 2020 - 4:08:28 PM


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  • HAL Id : hal-01449799, version 1


Fabienne Comte, Valentine Genon-Catalot. Laguerre basis for inverse problems . 2017. ⟨hal-01449799v1⟩



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