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Group Theoretical Study on Geodesics for the Elliptical Models

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

We consider the geodesic equation on the elliptical model, which is a generalization of the normal model. More precisely, we characterize this manifold from the group theoretical view point and formulate Eriksen’s procedure to obtain geodesics on normal model and give an alternative proof for it.

H. Inoue—Research Fellow of Japan Society for the Promotion of Science.

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References

  • Amari, S., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs. American Mathematical Society and Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  • Barbaresco, F.: Koszul Information geometry and Souriau geometric temperature/capacity of Lie group thermodynamics. Entropy 16, 4521–4565 (2014). doi:10.3390/e16084521

    Article  MathSciNet  Google Scholar 

  • Calvo, M., Oller, J.M.: A distance between elliptical distributions based in an embedding into the Siegel group. J. Comput. Appl. Math. 145, 319–334 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Calvo, M., Oller, J.M.: An explicit solution of information geodesic equations for the multivariate normal model. Stat. Decis. 9, 119–138 (1991)

    MathSciNet  MATH  Google Scholar 

  • Eriksen, P.S.: Geodesics connected with the Fisher metric on the multivariate normal manifold, pp. 225–229. Proceedings of the GST Workshop, Lancaster (1987)

    Google Scholar 

  • Helgason, S.: Differential Geometry and Symmetric Spaces. Academic Press, New York and London (1962)

    MATH  Google Scholar 

  • Imai, T., Takaesu, A., Wakayama, M.: Remarks on geodesics for multivariate normal models. J. Math-for-Ind. 3(2011B–6), 125–130 (2011B)

    MathSciNet  MATH  Google Scholar 

  • Muirhead, R.J.: Aspects of Multivariate Statistical Theory. Wiley, New York (1982)

    Book  MATH  Google Scholar 

  • Rao, C.R.: Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81–91 (1945)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Fukuoka, Japan

    Hiroto Inoue

Authors
  1. Hiroto Inoue
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Correspondence to Hiroto Inoue .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Inoue, H. (2015). Group Theoretical Study on Geodesics for the Elliptical Models. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_65

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_65

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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