The Annals of Mathematical Statistics

Statistical Models and Invariance

D. A. S. Fraser

Full-text: Open access

Abstract

Brillinger [2] gives necessary and sufficient conditions for a model to be invariant under a Lie group of transformations. The problems that can be handled by his conditions are surveyed, and found effectively to be restricted to one-dimensional problems amendable to Lindley's [8] method and to problems connected with conflicts between Bayes' and fiducial theory. The problem of finding the general model invariant under a given group is proposed. Brillinger's theorem produces differential equations for the model. A general solution can be obtained by direct methods.

Article information

Source
Ann. Math. Statist., Volume 38, Number 4 (1967), 1061-1067.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698775

Digital Object Identifier
doi:10.1214/aoms/1177698775

Mathematical Reviews number (MathSciNet)
MR214173

Zentralblatt MATH identifier
0161.38003

JSTOR
links.jstor.org

Citation

Fraser, D. A. S. Statistical Models and Invariance. Ann. Math. Statist. 38 (1967), no. 4, 1061--1067. doi:10.1214/aoms/1177698775. https://projecteuclid.org/euclid.aoms/1177698775


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