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Theses

Inférence non-paramétrique pour des interactions poissoniennes

Abstract : The subject of this thesis is the study of some adaptive nonparametric statistical problems in the framework of a Poisson interactions model. Such models are used, for instance, in neurosciences to analyze interactions between two neurons through their spikes emission during the recording of the brain activity or in genomics to study favored or avoided distances between two motifs along a genome. In this setting, we naturally introduce a so-called reproduction function that allows to quantify the favored positions of the motifs and which is considered as the intensity of a Poisson process. Our first interest is the estimation of this function assumed to be well localized. We propose a data-driven wavelet thresholding estimation procedure that is optimal from oracle and minimax points of view. Simulations and an application to genomic data from the bacterium E. coli allow us to show the good practical behavior of our procedure. Then, we deal with associated problems on tests which consist in testing the nullity of the reproduction function. For this purpose, we build a minimax optimal testing procedure on weak Besov spaces and we provide some simulations showing good practical performances of our procedure. Finally, we extend this work with the study of a high-dimensional discrete setting of our previous model by proposing an adaptive Lasso-type procedure.
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Submitted on : Tuesday, June 18, 2013 - 4:02:27 PM
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Laure Sansonnet. Inférence non-paramétrique pour des interactions poissoniennes. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2013. Français. ⟨NNT : 2013PA112084⟩. ⟨tel-00835427⟩

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