Mathematical Sciences: Location of Outliers in Structured Data

统计研究将在基于“元素集”的数据中寻找异常值。这涉及到将许多模型拟合到数据中，每个模型都精确地拟合到原始数据的最小子集，并以合适的方式组合来自这些元素集的信息，以便在一次传递中可靠地识别多个异常值。对于多元回归模型中的多元数据和其他类型的结构化数据，将研究该方法与更传统的方法之间的联系以及高分解点和可接受的效率。在回归和线性规划的单纯形算法的元素集之间的计算意义和代数联系将被探讨。

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.