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Information, Ancillarity and Conditional Inference

  • Shun-ichi Amari
Part of the Lecture Notes in Statistics book series (LNS, volume 28)

Abstract

The present chapter studies the amount of information carried by a statistic t(x) from the geometrical point of view. The amount of information plays a fundamental role in parameter estimation and statistical hypothesis testing. Higher-order asymptotic sufficiency, higher-order asymptotic ancillarity, and conditional information are defined in the beginning. Then, the performance of asymptotic conditional inference is studied, and the role of an asymptotic ancillary statistic is elucidated therefrom. We give an answer at least from the asymptotic point of view to the problem on which ancillary statistics one should condition when there are a number of ancillaries. Finally, the sufficient vector statistic x is decomposed into component statistics of geometrical character according as the magnitude of the amount of information.

Keywords

Fisher Information Information Loss Exponential Family Conditional Covariance Curvature Direction 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Shun-ichi Amari
    • 1
  1. 1.Faculty of Engineering Department of Mathematical Engineering and Information PhysicsUniversity of TokyoTokyoJapan

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