## Statistical Science

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

### Saddlepoint Methods and Statistical Inference

#### 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

#### See also

- See Comment: O. E. Barndorff-Nielsen. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 228--229.Project Euclid: euclid.ss/1177012907
- See Comment: H. E. Daniels. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 229--229.Project Euclid: euclid.ss/1177012908
- See Comment: Philip Hougaard. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 230--231.Project Euclid: euclid.ss/1177012909
- See Comment: D. V. Hinkley, S. Wang. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 232--233.Project Euclid: euclid.ss/1177012910
- See Comment: Luke Tierney. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 233--234.Project Euclid: euclid.ss/1177012911
- See Comment: Robert E. Kass. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 234--236.Project Euclid: euclid.ss/1177012912
- See Comment: Ann F. S. Mitchell. [Saddlepoint Methods and Statistical Inference]: Comment. Statist. Sci., Volume 3, Number 2 (1988), 237--237.Project Euclid: euclid.ss/1177012913
- See Comment: N. Reid. [Saddlepoint Methods and Statistical Inference]: Rejoinder. Statist. Sci., Volume 3, Number 2 (1988), 237--238.Project Euclid: euclid.ss/1177012914