Statistical Science

The Geometry of Asymptotic Inference

Robert E. Kass

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Abstract

Geometrical foundations of asymptotic inference are described in simple cases, without the machinery of differential geometry. A primary statistical goal is to provide a deeper understanding of the ideas of Fisher and Jeffreys. The role of differential geometry in generalizing results is indicated, further applications are mentioned, and geometrical methods in nonlinear regression are related to those developed for general parametric families.

Article information

Source
Statist. Sci., Volume 4, Number 3 (1989), 188-219.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177012480

Digital Object Identifier
doi:10.1214/ss/1177012480

Mathematical Reviews number (MathSciNet)
MR1015274

Zentralblatt MATH identifier
0955.62513

JSTOR
links.jstor.org

Keywords
Information distance measures Jeffreys' prior Bayes factor orthogonal parameters curved exponential family statistical curvature approximate sufficiency ancillary statistic nonlinear regression

Citation

Kass, Robert E. The Geometry of Asymptotic Inference. Statist. Sci. 4 (1989), no. 3, 188--219. doi:10.1214/ss/1177012480. https://projecteuclid.org/euclid.ss/1177012480


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See also

  • See Comment: S. I. Amari. [The Geometry of Asymptotic Inference]: Comment. Statist. Sci., Volume 4, Number 3 (1989), 220--222.
  • See Comment: O. E. Barndorff-Nielsen. [The Geometry of Asymptotic Inference]: Comment. Statist. Sci., Volume 4, Number 3 (1989), 222--227.
  • See Comment: Jose M. Bernardo. [The Geometry of Asymptotic Inference]: Comment: On Multivariate Jeffreys' Priors. Statist. Sci., Volume 4, Number 3 (1989), 227--229.
  • See Comment: C. R. Rao. [The Geometry of Asymptotic Inference]: Comment. Statist. Sci., Volume 4, Number 3 (1989), 229--231.
  • See Comment: N. Reid, D. A. S. Fraser. [The Geometry of Asymptotic Inference]: Comment. Statist. Sci., Volume 4, Number 3 (1989), 231--233.
  • See Comment: Robert E. Kass. [The Geometry of Asymptotic Inference]: Rejoinder. Statist. Sci., Volume 4, Number 3 (1989), 233--234.

Corrections

  • See Correction: O. E. Barndorff-Nielsen. Correction Note: Comment by O. E. Barndorff-Nielsen on "The Geometry of Asymptotic Inference," by R. E. Kass, 1989, Vol. 4, 222-227. Statist. Sci., Volume 5, Number 3 (1990), 370--370.