Contributions à l'inférence statistique dans les modèles de régression partiellement linéaires additifs

Abstract : Parametric regression models provide powerful tools for analyzing practical data when the models are correctly specified, but may suffer from large modelling biases when structures of the models are misspecified. As an alternative, nonparametric smoothing methods eases the concerns on modelling biases. However, nonparametric models are hampered by the so-called curse of dimensionality in multivariate settings. One of the methods for attenuating this difficulty is to model covariate effects via a partially linear structure, a combination of linear and nonlinear parts. To reduce the dimension impact in the estimation of the nonlinear part of the partially linear regression model, we introduce an additive structure of this part which induces, finally, a partially linear additive model. Our aim in this work is to establish some limit results pertaining to various parameters of the model (consistency, rate of convergence, asymptotic normality and iterated logarithm law) and to construct some hypotheses testing procedures related to the model structure, as the additivity of the nonlinear part, and to its parameters.
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Khalid Chokri. Contributions à l'inférence statistique dans les modèles de régression partiellement linéaires additifs. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066439⟩. ⟨tel-01127559⟩

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