Skip to Main content Skip to Navigation

Estimation non-paramétrique adaptative pour des modèles bruités

Abstract : In this thesis, we are interested in nonparametric adaptive estimation problems of density in the convolution model. This framework matches additive measurement error models, which means we observe a noisy version of the random variable of interest. To carry out our study, we follow the paradigm of model selection developped by Birgé & Massart or criterion based on Lepski's method. The thesis is divided into two parts. In the first one, the main goal is to build adaptive estimators in the convolution model when both random variables of interest and errors are distributed on the nonnegative real line. Thus we propose adaptive estimators of the density along with the survival function, then of linear functionals of the target density. This part ends with a linear density aggregation procedure. The second part of the thesis deals with adaptive estimation of density in the convolution model when the distribution is unknown and distributed on the real line. To make this problem identifiable, we assume we have at hand either a preliminary sample of the noise or we observe repeated data. So, we can derive adaptive estimation with mild assumptions on the noise distribution. This methodology is then applied to linear mixed models and to the problem of density estimation of the sum of random variables when the latter are observed with an additive noise.
Complete list of metadatas

Cited literature [142 references]  Display  Hide  Download
Contributor : Abes Star :  Contact
Submitted on : Monday, September 18, 2017 - 11:55:18 AM
Last modification on : Friday, March 27, 2020 - 2:29:09 AM


Version validated by the jury (STAR)


  • HAL Id : tel-01589142, version 1



Gwennaëlle Mabon. Estimation non-paramétrique adaptative pour des modèles bruités. Mathématiques générales [math.GM]. Université Sorbonne Paris Cité, 2016. Français. ⟨NNT : 2016USPCB020⟩. ⟨tel-01589142⟩



Record views


Files downloads