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B0416
Title: Backward nested subspaces: Asymptotics, two-sample tests and applications Authors:  Benjamin Eltzner - Georg-August-University of Goettingen (Germany) [presenting]
Abstract: Dimension reduction is an important tool in multivariate statistical analysis, aiming at a description of the relevant modes of variation in a data set. For data on manifolds or stratified spaces, dimension reduction becomes more involved as forward and backward methods must be distinguished. We introduce the notion of backward nested subspaces as a generalization of principal nested spheres. For such general families of estimated nested subspaces we provide asymptotic results and inferential tools. We illustrate the power of our methods by simulations and applications to data.