Dimension Reduction, Model Selection and Classification in Functional Data Analysis.

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Functional data analysis aims to model and analyze data sets where a datum is a random function, e.g. a curve or a high dimensional image. Due to the fast growth of modern data collection methods, such data sets become more and more prevalent in many biological, medical and industrial applications. Functional data are viewed as infinite dimensional vectors in a functional space, and are usually observed on discrete points and measured with error. Due to the infinite dimensional nature of functional data, dimension reduction is essential for visualizing, modeling and making inference on these data. In the proposed project, the investigator will study new, computationally efficient dimension reduction methods for functional data based on spline approximations, and use asymptotic theory to develop new statistical devices for model selection and inference. The investigator will also study classification problems in functional data, by combining the proposed dimension reduction techniques with modern machine learning methods.The proposed research is motivated by data from colon carcinogenesis experiments, hypertension studies, AIDS clinical trials and functional magnetic resonance imaging experiments. The proposed project will benefit the society by advancing knowledge in these scientific fields. To achieve broader dissemination of the research results, the investigator will provide free and user friendly software to all scientific researchers. A new course on functional data analysis will be developed in the investigator's institute. The new course aims to nurture the ability of students to analyze real and innovative data sets and help them gain deeper understanding of modern statistical methods and theory.