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Title: Prediction with robust mixtures of Gaussian local mapping Authors:  Naisyin Wang - University of Michigan (United States) [presenting]
Abstract: The uses of mixtures provide a powerful tool to simplify the task of modeling complicated associations between variables. Data with similar associations are grouped together and simple estimation techniques can be applied on each cluster. This strategy also allows flexibility in distinguishing structures of interest. However, recovering the appropriate structure embedded in mixture is not a trivial task under certain circumstances. The presence of outliers might have severe impacts on forming the suitable clusters. Thus, robust consideration is particularly important under non-standard scenarios. We propose a robust mixture regression approach coupling with the use of trimmed likelihood to established structured functional-regression modeling of scalar responses and functional predictors. Our modeling strategies form a family of assumed models. Model-averaging, model-selection and their hybrids are then naturally incorporated under a unified framework into a modified Expectation-Maximization algorithm. The outcomes provide the estimated parameters in the most favorable assumed model that satisfies pre-determined criteria and then is used for prediction. We provide theoretical justifications behind the proposed procedures and illustrate their numerical performances using synthetic and real-world data sets.