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August, 1967 Statistical Models and Invariance
D. A. S. Fraser
Ann. Math. Statist. 38(4): 1061-1067 (August, 1967). DOI: 10.1214/aoms/1177698775


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.


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D. A. S. Fraser. "Statistical Models and Invariance." Ann. Math. Statist. 38 (4) 1061 - 1067, August, 1967.


Published: August, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0161.38003
MathSciNet: MR214173
Digital Object Identifier: 10.1214/aoms/1177698775

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 4 • August, 1967
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