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A Nonparametric Theory of Statistics on Manifolds

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Limit Theorems in Probability, Statistics and Number Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 42))

Abstract

An expository account of the recent theory of nonparametric inference on manifolds is presented here, with outlines of proofs and examples. Much of the theory centers around Fréchet means; but functional estimation and classification methods using nonparametric Bayes theory are also indicated. Applications in paleomagnetism, morphometrics and medical diagnostics illustrate the theory.

2010 Mathematics Subject Classification. Primary 62G20; Secondary 62G05, 62G10, 62H35, 62P10

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Acknowledgements

The author wishes to thank the referee for helpful suggestions. This research is supported by NSF grant DMS 1107053.

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Authors and Affiliations

  1. Department of Mathematics, The University of Arizona, Tucson, AZ, 85721, USA

    Rabi Bhattacharya

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  1. Rabi Bhattacharya
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Correspondence to Rabi Bhattacharya .

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Editors and Affiliations

  1. Mathematics Faculty, Ruhr-University Bochum, Universitätstr. 150, Bochum, 44780, Germany

    Peter Eichelsbacher

  2. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Guido Elsner

  3. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Holger Kösters

  4. Institute for Mathematical Statistics, University of Münster, Einsteinstrasse 62, Münster, 48149, Germany

    Matthias Löwe

  5. Mathematics Institute, University of München, Theresienstr. 39, München, 80333, Germany

    Franz Merkl

  6. Centre for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85747, Germany

    Silke Rolles

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Dedicated to Friedrich Götze on the Occasion of his Sixtieth Birthday

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Bhattacharya, R. (2013). A Nonparametric Theory of Statistics on Manifolds. In: Eichelsbacher, P., Elsner, G., Kösters, H., Löwe, M., Merkl, F., Rolles, S. (eds) Limit Theorems in Probability, Statistics and Number Theory. Springer Proceedings in Mathematics & Statistics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36068-8_9

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