Geometry and marginals

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    It is known that observations of a real-valued random variable defined over a smooth manifold M can be used to make inferences about M, at least when M is a curve or surface. We refine and extend the underlying asymptotic results and remove the condition dim M <= 2. New examples of nonsmoothness in marginals are described in detail for dim M = 3, 4, and methods are given for calculations in general. (C) 2005 Published by Elsevier Inc.
    Original languageEnglish
    Pages (from-to)194-208
    JournalJournal of Multivariate Analysis
    Publication statusPublished - 2007


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