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Estimation dans le modèle d'empilement avec application aux mesures de la fluorescence résolue en temps

Tabea Rebafka 1, 2
2 LOAD - Laboratoire Outils d'Analyse des Données
DM2I - Département Métrologie Instrumentation & Information : DRT/LIST/DM2I
Abstract : This thesis studies the so-called pile-up model and proposes adequate estimators. An observation of the pile-up model is the minimum of a random number of variables from the target distribution. The pile-up distribution is the result of a non linear distortion of the target distribution. The goal is to identify the target distribution from observations of the pile-up model. The model is motivated by the application TCSPC in time-resolved fluorescence, where the extent of distortion is determined by a tuning parameter selected by the user. A study of the Cramér-Rao bound provides the best value of this parameter. Simulations with a Gibbs sampler confirm the theoretical results on a significant reduction of the variance compared to the current practice. Another estimator is proposed by a maximum likelihood approach based on a new contrast and whose computation time is satisfactory. In many cases the estimator can be computed by an EM-type algorithm. Furthermore, the consistence as well as the limit distribution is established. A comparison to the current practice in fluorescence shows that a reduction of the acquisition time by a factor 10 is possible. In the last part, a non parametric estimator of the mixing density of an infinite mixture of exponential densities is proposed. The estimator is based on orthogonal series and it is shown to be optimal in the sense that its mean integrated square error achieves the minimax rate on some specific smoothness spaces. Moreover, the estimator can be adapted to the pile-up model, when the target distribution is an infinite exponential mixture.
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Submitted on : Wednesday, May 19, 2010 - 8:00:00 AM
Last modification on : Friday, July 31, 2020 - 10:44:09 AM
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Tabea Rebafka. Estimation dans le modèle d'empilement avec application aux mesures de la fluorescence résolue en temps. Traitement du signal et de l'image [eess.SP]. Télécom ParisTech, 2009. Français. ⟨NNT : 2009ENST0018⟩. ⟨pastel-00005715⟩

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