Statistical Science

Saddlepoint Methods and Statistical Inference

N. Reid

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Abstract

This paper reviews Daniels' saddlepoint approximation to the distribution of the mean of a random sample, and the many aspects of second order asymptotic inference that have been developed from it. These include Barndorff-Nielsen's approximation to the distribution of the maximum likelihood estimate, Bartlett factors for the likelihood ratio statistic and approximations to predictive and conditional likelihood. The emphasis is on statistical applications of the saddlepoint method. The intention is to provide fairly broad coverage of the literature and to indicate possibilities for future development. An annotated bibliography is included.

Article information

Source
Statist. Sci., Volume 3, Number 2 (1988), 213-227.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177012906

Digital Object Identifier
doi:10.1214/ss/1177012906

Mathematical Reviews number (MathSciNet)
MR968390

Zentralblatt MATH identifier
0955.62541

JSTOR
links.jstor.org

Keywords
Asymptotic expansion Bartlett factor conditional inference Edgeworth series exponential families likelihood ratio statistic maximum likelihood estimate saddlepoint approximation score statistic second order approximations

Citation

Reid, N. Saddlepoint Methods and Statistical Inference. Statist. Sci. 3 (1988), no. 2, 213--227. doi:10.1214/ss/1177012906. https://projecteuclid.org/euclid.ss/1177012906


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See also

  • See Comment: O. E. Barndorff-Nielsen. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 228--229.
  • See Comment: H. E. Daniels. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 229--229.
  • See Comment: Philip Hougaard. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 230--231.
  • See Comment: D. V. Hinkley, S. Wang. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 232--233.
  • See Comment: Luke Tierney. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 233--234.
  • See Comment: Robert E. Kass. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 234--236.
  • See Comment: Ann F. S. Mitchell. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 237--237.
  • See Comment: N. Reid. [Saddlepoint Methods and Statistical Inference]: Rejoinder. Statist. Sci., Volume 3, Number 2 (1988), 237--238.