Mathematical Sciences: Location of Outliers in Structured Data

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Statistical research will be conducted on finding outliers in data that is based on "elemental sets". This involves fitting many models to the data, each an exact fit to a minimally-sized subset of the original data, and combining the information from these elemental sets in suitable ways to identify multiple outliers reliably and in a single pass. The connection between this method and more traditional methods as well as high breakdown points and acceptable efficiency will be investigated for multivariate data in the multivariate regression model and in other types of structured data. The computational implications and the algebraic connections between elemental sets in regression and the simplex algorithm of linear programming will be explored.