Inférence statistique dans les modèles mixtes à dynamique Markovienne

Abstract : The first part of this thesis deals with maximum likelihood estimation in Markovian mixed-eff ects models. More precisely, we consider mixed-eff ects hidden Markov models and mixed-eff ects diff usion models. In Chapter 2, we combine the Baum-Welch algorithm and the SAEM algorithm to estimate the population parameters in mixed-eff ects hidden Markov models. We also propose some speci c procedures to estimate the individual parameters and the sequences of hidden states. We study the properties of the proposed methodologies on simulated datasets and we present an application to real daily seizure count data. In Chapter 3, we fi rst suggest mixed-eff ects diffusion models for population pharmacokinetics. We estimate the parameters of these models by combining the SAEM algorithm with the extended Kalman filter. Then, we study the asymptotic properties of the maximum likelihood estimate in some mixed-effects diff usion models continuously observed on a fi xed time interval when the number of subjects tends to infi nity. Chapter 4 is dedicated to variable selection in general mixed-e ffects models. We propose a BIC adapted to the asymptotic context where both of the number of subjects and the number of observations per subject tend to infi nity. We illustrate this procedure with some simulations.
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Contributor : Maud Delattre <>
Submitted on : Sunday, December 16, 2012 - 1:25:43 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
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Maud Delattre. Inférence statistique dans les modèles mixtes à dynamique Markovienne. Applications [stat.AP]. Université Paris Sud - Paris XI, 2012. Français. ⟨tel-00765708⟩

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