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Modèles de régression pour données fonctionnelles hétérogènes : application à la modélisation de données de spectrométrie dans le moyen infrarouge

Abstract : In many application fields, data corresponds to curves. This work focuses on the analysis of spectrometric curves, composed of hundreds of ordered variables that corresponds to the absorbance values measured for each wavenumber. In this context, an automatic statistical procedure is developped, that aims at building a prediction model taking into account the heterogeneity of the observed data. More precisely, a diagnosis tool is built in order to predict a metabolic disease from spectrometric curves measured on a population composed of patients with differents profile. The procedure allows to select portions of curves relevant for the prediction and to build a partition of the data and a sparse predictive model simultaneously, using a mixture of penalized regressions suitable for functional data. In order to study the complexity of the data and of the application case, a method to better understand and display the interactions between variables is built. This method is based on the study of the covariance matrix structure, and aims to highlight the dependencies between blocks of variables. A medical example is used to present the method and results, and allows the use of specific visualization tools.
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Marie Morvan. Modèles de régression pour données fonctionnelles hétérogènes : application à la modélisation de données de spectrométrie dans le moyen infrarouge. Statistiques [math.ST]. Université Rennes 1, 2019. Français. ⟨NNT : 2019REN1S097⟩. ⟨tel-02888695⟩

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