2 research outputs found

    Semiparametric topographical mixture models with symmetric errors

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    Motivated by the analysis of a Positron Emission Tomography (PET) imaging data considered in Bowen et al. (2012), we introduce a semiparametric topographical mixture model able to capture the characteristics of dichotomous shifted response-type experiments. We propose a local estimation procedure, based on the symmetry of the local noise, for the proportion and locations functions involved in the proposed model. We establish under mild conditions the minimax properties and asymptotic normality of our estimators when Monte Carlo simulations are conducted to examine their finite sample performance. Finally a statistical analysis of the PET imaging data in Bowen et al. (2012) is illustrated for the proposed method.Comment: 19 figure

    Model selection and estimation in high dimensional settings

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    Several statistical problems can be described as estimation problem, where the goal is to learn a set of parameters, from some data, by maximizing a criterion. These type of problems are typically encountered in a supervised learning setting, where we want to relate an output (or many outputs) to multiple inputs. The relationship between these outputs and these inputs can be complex, and this complexity can be attributed to the high dimensionality of the space containing the inputs and the outputs; the existence of a structural prior knowledge within the inputs or the outputs that if ignored may lead to inefficient estimates of the parameters; and the presence of a non-trivial noise structure in the data. In this thesis we propose new statistical methods to achieve model selection and estimation when there are more predictors than observations. We also design a new set of algorithms to efficiently solve the proposed statistical models. We apply the implemented methods to genetic data sets of cancer patients and to some economics data.Ph.D