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Estimation par ondelettes dans les modèles partiellement linéaires

Irène Gannaz 1 
1 SMS - Statistique et Modélisation Stochatisque
LJK - Laboratoire Jean Kuntzmann
Abstract : This dissertation is concerned with the use of wavelet methods in semiparametric partially linear models. These models are composed by a linear component with unknown regression coefficients and an unknown nonparametric function. The aim is to estimate both of the predictors, possibly under the presence of correlation. A wavelet thresholding based procedure is built to estimate the nonparametric part of the model using a penalized least squares criterion. We establish a connection between different thresholding schemes and M-estimators in linear models with outliers, where the wavelet coefficients of the nonparametric part of the model are considered as outliers. We also propose an estimate for the noise variance. Some asymptotic results of the estimates of both the parametric and the nonparametric part are given. Their behavior is close to optimality, up to a logarithmic factor, under usual restrictions for the correlation between variables. Simulations illustrate the properties of the proposed methodology and compare it with existing methods. An application to real data from functional IRM is also presented. The last part of this work deals with the extension to nonequidistant observations for the nonparametric part, comparing in particular via simulations nonparametric estimation procedures.
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Submitted on : Friday, December 14, 2007 - 1:30:09 PM
Last modification on : Friday, March 25, 2022 - 11:09:31 AM
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  • HAL Id : tel-00197146, version 1



Irène Gannaz. Estimation par ondelettes dans les modèles partiellement linéaires. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2007. Français. ⟨tel-00197146⟩



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