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Segmentation de processus avec un bruit autorégressif

Abstract : We propose to study the methodology of autoregressive processes segmentation under both its theoretical and practical aspects. “Segmentation” means here inferring multiple change-points corresponding to mean shifts. We consider autoregression parameters as nuisance parameters, whose estimation is considered only for improving the segmentation.From a theoretical point of view, we aim to keep some asymptotic properties of change-points and other parameters estimators. From a practical point of view, we have to take into account the algorithmic constraints to get the optimal segmentation. To meet these requirements, we propose a method based on robust estimation techniques, which allows a preliminary estimation of the autoregression parameters and then the decorrelation of the process. The aim is to get our problem closer to the segmentation in the case of independent observations. This method allows us to use efficient algorithms. It is based on asymptotic results that we proved. It allows us to propose adapted and well-founded number of changes selection criteria. A simulation study illustrates the method.
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Submitted on : Thursday, November 5, 2015 - 9:52:06 AM
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Souhil Chakar. Segmentation de processus avec un bruit autorégressif. Statistiques [math.ST]. Université Paris Sud - Paris XI, 2015. Français. ⟨NNT : 2015PA112196⟩. ⟨tel-01224745⟩

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