Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T01:59:42.286Z Has data issue: false hasContentIssue false

On group representations and invariant stochastic processes

Published online by Cambridge University Press:  24 October 2008

A. D. Mclaren
Affiliation:
Statistical Laboratory, Department of Mathematics, University of Manchester

Abstract

The theory of group representations is explored with regard to statistical applications. Ease of analysis depends rather critically on the amount of symmetry present and this point is examined in detail. ‘ Stationarity’ assumptions are considered for a finite number of variates, with examples of their use in experimental situations.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1963

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hannan, E. J., Application of the representation theory of groups and algebras to some statistical problems. Research Reports (Part I), Summer Research Institute, Australian Mathematical Society (1961).Google Scholar
(2)Heine, V., Group theory in quantum mechanics (Pergamon; London, 1960).Google Scholar
(3)James, A. T., Relationship algebra of an experimental design. Ann. Math. Statist. 28 (1957), 9931002.CrossRefGoogle Scholar
(4)Johnston, D. F., Group theory in solid state physics. Reports on Progress in Physics, 23 (1960), 66153.CrossRefGoogle Scholar
(5)Lehmann, E. L., Testing statistical hypotheses (Wiley; New York, 1959).Google Scholar
(6)Littlewood, D. E., Theory of group characters (Oxford, 1950).Google Scholar
(7)Murnaghan, F. D., Theory of group representations (Johns Hopkins; Baltimore, 1938).Google Scholar
(8)Rao, , Radhakrishna, C.. Tests of significance in multivariate analysis. Biometrika, 35 (1948), 6263.Google Scholar