Proposal: 9505583 PI: Ker-Chau Li Institution: UCLA Title: High Dimensional Data Analysis Abstract: The research concerns the development of new statistical methods for exploring nonlinearity in high dimensional data. Two tools, sliced inverse regression (SIR) and principal Hessian directions (PHD), have been developed based on a dimension reduction theory which underlies the investigator's approach in the high-Dimension area. To continue this line of research, the investigator studies several new problems which have more complicated structures than the basic regression formulation. The research topics include the generalization of SIR/PHD to multiple outcomes, development of PHD-based tree-structured methods, study of visualization for mathematical/physical/computer models, and analysis of nonlinear time series data. The research takes a combination of dynamic graphics, computation, and statistical theory to study high dimensional data. Dimensionality is one of the most challenging problems in maly scientific areas today. Immediate applications of these research results include analysis of longitudinal data in biomedical, socio-economic, or industrial studies, and groundwater modeling in hydrological studies.
