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Bootstrapping Descriptors for Non-Euclidean Data

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

For data carrying a non-Euclidean geometric structure it is natural to perform statistics via geometric descriptors. Typical candidates are means, geodesics, or more generally, lower dimensional subspaces, which carry specific structure. Asymptotic theory for such descriptors is slowly unfolding and its application to statistical testing usually requires one more step: Assessing the distribution of such descriptors. To this end, one may use the bootstrap that has proven to be a very successful tool to extract inferential information from small samples. In this communication we review asymptotics for descriptors of manifold valued data and study a non-parametric bootstrap test that aims at a high power, also under the alternative.

B. Eltzner and S. Huckemann—Acknowledging the Niedersachsen Vorab of the Volkswagen Foundation.

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Authors and Affiliations

  1. Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences, University of Goettingen, Goettingen, Germany

    Benjamin Eltzner & Stephan Huckemann

Authors
  1. Benjamin Eltzner
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  2. Stephan Huckemann
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Correspondence to Benjamin Eltzner .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Eltzner, B., Huckemann, S. (2017). Bootstrapping Descriptors for Non-Euclidean Data. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

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