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Differential geometry of statistical inference

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Probability Theory and Mathematical Statistics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1021))

Abstract

A higher-order asymptotic theory of statistical inference is presented in a unified manner in the differential-geometrical framework. The first-, second- and third-order efficiencies of estimators are obtained in terms of the curvatures and connections of submanifolds related to both the model and estimator. The first-, second and third- order powers of a two-sided (unbiased) test is also obtained in terms of the curvature and the intersecting angle of the boundary of the critical region.

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References

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Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Tokyo, 7-3-1 Bunkyo-ku, 113, Tokyo, Japan

    Shun-ichi Amari

Authors
  1. Shun-ichi Amari
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Editors and Affiliations

  1. Steklov Mathematical Institute of the Academy of Sciences of the USSR, Vavilov str. 42, Moscow, 117966, USSR

    Jurii V. Prokhorov

  2. Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima- ku, Tokyo, Japan

    Kiyosi Itô

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© 1983 Springer-Verlag Berlin Heidelberg

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Amari, Si. (1983). Differential geometry of statistical inference. In: Prokhorov, J.V., Itô, K. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072900

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  • DOI: https://doi.org/10.1007/BFb0072900

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12718-5

  • Online ISBN: 978-3-540-38701-5

  • eBook Packages: Springer Book Archive

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