Régularisation et sélection de variables par le biais de la vraisemblance pénalisée

Abstract : We are interested in variable sélection in linear régression models. This research is motivated by recent development in microarrays, proteomics, brain images, among others. We study this problem in both frequentist and bayesian viewpoints.In a frequentist framework, we propose methods to deal with the problem of variable sélection, when the number of variables is much larger than the sample size with a possibly présence of additional structure in the predictor variables, such as high corrélations or order between successive variables. The performance of the proposed methods is theoretically investigated ; we prove that, under regularity conditions, the proposed estimators possess statistical good properties, such as Sparsity Oracle Inequalities, variable sélection consistency and asymptotic normality.In a Bayesian Framework, we propose a global noninformative approach for Bayesian variable sélection. In this thesis, we pay spécial attention to two calibration-free hierarchical Zellner’s g-priors. The first one is the Jeffreys prior which is not location invariant. A second one avoids this problem by only considering models with at least one variable in the model. The practical performance of the proposed methods is illustrated through numerical experiments on simulated and real world datasets, with a comparison betwenn Bayesian and frequentist approaches under a low informative constraint when the number of variables is almost equal to the number of observations.
Document type :
Theses
Complete list of metadatas

Cited literature [101 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00661689
Contributor : Abes Star <>
Submitted on : Friday, January 20, 2012 - 2:03:04 PM
Last modification on : Friday, May 17, 2019 - 10:41:18 AM
Long-term archiving on : Wednesday, December 14, 2016 - 12:00:35 AM

File

VD2_ELANBARI_MOHAMMED_14122011...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00661689, version 1

Collections

Citation

Mohammed El Anbari. Régularisation et sélection de variables par le biais de la vraisemblance pénalisée. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI; Université Cadi Ayyad (Marrakech, Maroc), 2011. Français. ⟨NNT : 2011PA112297⟩. ⟨tel-00661689⟩

Share

Metrics

Record views

714

Files downloads

2873