Topics in multivariate nonparametric and robust methods

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This project will develop some novel statistical tools for the analysis of univariate, multivariate and also very high-dimensional data arising from medical research, environmental studies, images, and industrial processes. This includes for example images of faces, handwriting, human gene, world wide web, social networks, disease epidemics, cancer screening and prevention trials, neuronal, and lifetime data, etc. Some of the tools for analyzing such data involve ranking and sorting of multivariate data by using a concept of data depth. Data depth is a measure of centrality of a given high dimensional point within a high dimensional data set.