Mathematical Sciences: Robust Estimation of Multivariate Location and Shape in High Dimension

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This project will develop computationally efficient, robust, affine-equivariant estimators of multivariate location and shape for use in multivariate analysis and for identification of high leverage points in robust regression. This problem has proved to be computationally quite challenging---reliable solutions were possible with previous methods only for small samples and low dimension. We have developed methods that greatly increase the effectiveness of these procedures and propose to develop these methods further, including the adaptation to massively parallel architectures. The goal, which seems to be in reach, is to obtain reliable, estimates in a few seconds, compared to the many hours of computation time now required. The detection of unusual observations and clusters of observations is an important part of any effective statistical analysis. Such observations may be mistakes or may represent important new phenomena. For data that consists of many simultaneous measurements, this goal has to date been out of reach of the best statistical methods. We have developed techniques that make this goal practical, and, under this project, we will further develop them, together with their computer implementations.