Validation croisée et pénalisation pour l'estimation de densité

Abstract : This thesis takes place in the density estimation setting from a nonparametric and nonasymptotic point of view. It concerns the statistical algorithm selection problem which generalizes, among others, the problem of model and bandwidth selection. We study classical procedures, such as penalization or resampling procedures (in particular V-fold cross-validation), which evaluate an algorithm by estimating its risk. We provide, thanks to concentration inequalities, an optimal penalty for selecting a linear estimator and we prove oracle inequalities and adaptative properties for resampling procedures. Moreover, new resampling procedure, based on estimator comparison by the mean of robust tests, is introduced as an alternative to procedures relying on the unbiased risk estimation principle. A second goal of this work is to compare these procedures from a theoretical point of view and to understand the role of V for V-fold penalization. We validate these theoretical results on empirical studies.
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Nelo Magalhães. Validation croisée et pénalisation pour l'estimation de densité. Probabilités [math.PR]. Université Paris Sud - Paris XI, 2015. Français. ⟨NNT : 2015PA112100⟩. ⟨tel-01164581⟩

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