## The Annals of Mathematical Statistics

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

### Statistical Models and Invariance

#### 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