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Differential geometry of statistical inference

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Vector Field
  • Tangent Space
  • Statistical Inference
  • Critical Region
  • Maximum Likelihood Estimator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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

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