Goodness-of-fit testing and independent component analysis with applications to cognitive neuroscience

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Statistics is a powerful discipline that deals with gaining information from data and it has been applied to many other fields of science. In that perspective, neuroscience is a new and fascinating field of research that focuses on the study of the animal or human brain behaviour. And it is very naturally that statisticians have begun to offer their skills to researchers of the field. This proposition is devoted to add my contribution to this effort. The present proposal contains two parts. The first one is dedicated to the development of new goodness-of-fit procedures, using empirical characteristic function based processes or developed in the context of multivariate time series models. Another aspect is the development of new innovative Independent Component Analysis (ICA) Methods. The tools built in this part will be used to help understanding our brain's behaviour through model building of functional Magnetic Resonance Imaging (fMRI) data. For example, ICA are recent and powerful exploratory techniques exploiting the dependencies between many random variables. They can be used to explore the huge data sets collected during fMRI experiments and they can be seen as a good complement to other more confirmatory techniques. All the methods developed in this last project will be implemented into the AnalyzeFMRI R package.