# Adaptive deconvolution on the nonnegative real line

Abstract : In this paper we consider the problem of adaptive density or survival function estimation in an additive model defined by $Z = X + Y$ with $X$ independent of $Y$, when both random variables are nonnegative. We want to recover the distribution of $X$ (density or survival function) through $n$ observations of $Z$, assuming that the distribution of $Y$ is known. This issue can be seen as the classical statistical problem of deconvolution which has been tackled in many cases using Fourier-type approaches. Nonetheless, in the present case the random variables have the particularity to be $\mathbb{R}^+$ supported. Knowing that, we propose a new angle of attack by building a projection estimator with an appropriate Laguerre basis. We present upper bounds on the mean squared integrated risk of our density and survival function estimators. We then describe a nonparametric adaptive strategy for selecting a relevant projection space. The procedures are illustrated with simulated data and compared to the performances of more classical deconvolution setting using a Fourier approach.
Keywords :
Type de document :
Pré-publication, Document de travail
MAP5 2014-33. 2016
Domaine :

https://hal.archives-ouvertes.fr/hal-01076927
Contributeur : Gwennaëlle Mabon <>
Soumis le : mercredi 16 novembre 2016 - 16:16:37
Dernière modification le : samedi 18 février 2017 - 01:10:45
Document(s) archivé(s) le : jeudi 16 mars 2017 - 16:12:13

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Laguerredeconvolution.pdf
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• HAL Id : hal-01076927, version 3

### Citation

Gwennaëlle Mabon. Adaptive deconvolution on the nonnegative real line. MAP5 2014-33. 2016. <hal-01076927v3>

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