The Annals of Statistics

Asymptotics and the theory of inference

N. Reid

Full-text: Open access

Abstract

Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years provides an illustration of the interplay between techniques of approximation and statistical theory.

Article information

Source
Ann. Statist. Volume 31, Number 6 (2003), 1695-2095.

Dates
First available in Project Euclid: 16 January 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1074290325

Digital Object Identifier
doi:10.1214/aos/1074290325

Mathematical Reviews number (MathSciNet)
MR2036388

Zentralblatt MATH identifier
1042.62022

Subjects
Primary: 62-02: Research exposition (monographs, survey articles)
Secondary: 62E20: Asymptotic distribution theory 62F05: Asymptotic properties of tests

Keywords
Ancillarity approximation Bayesian inference conditioning Laplace approximation likelihood matching priors $p$* $p$-values $r$* saddlepoint approximation tail area tangent exponential model

Citation

Reid, N. Asymptotics and the theory of inference. Ann. Statist. 31 (2003), no. 6, 1695--2095. doi:10.1214/aos/1074290325. https://projecteuclid.org/euclid.aos/1074290325.


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