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Inférence statistique par lissage linéaire local pour une fonction de régression présentant des discontinuités

Abstract : In this thesis, we consider the change-point problems in nonparametric regression model: detection of change-points, estimation of the change-point parameters and segmentation of the regression function are investigated. The proposed method is based on a comparison of left and right one-sided smoothers. These smoothers are obtained by local linear regression. \par First, we propose an estimator of the jump size in the regression function when the location of the change-point is known. We derive the expression of its asymptotic MSE and its asymptotic normality. Next we propose an estimator of the location of the change-point and give its asymptotic distribution and corresponding rate of convergence. Afterwards, we are interested in testing for a change-point. The properties of the deviation process associated with the jump estimate process, allow to obtain the asymptotic distributions of some test statistics for a change-point. In the case where there are more than one change, we introduce a consistant algorithm to estimate the number of change-points together with their localizations. Finally, we propose a method for the estimation of a piecewise smooth regression fonction. We show that, provided discontinuities can be located with sufficient accuracy, our approach enjoys rates of convergence similar to those obtained in smooth case. For each of the proposed procedures, we provide numerical experiments that show evidence of the quality of the method and give some information about the dependence upon such parameters as the kernel and the bandwith.
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Submitted on : Wednesday, February 18, 2004 - 3:10:28 PM
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Zouhir Hamrouni. Inférence statistique par lissage linéaire local pour une fonction de régression présentant des discontinuités. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1999. Français. ⟨tel-00004840⟩

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