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ANOVA models with random effects: an approach via symmetry

Published online by Cambridge University Press:  14 July 2016

T. P. Speed
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Abstract

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

Keywords

COMPONENT OF VARIANCEGROUP INVARIANCEEXCHANGEABILITYGENERALISED SPECTRUM ANALYSIS
Type
Part 6—Allied Stochastic Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 355 - 368
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Aigner, M. (1979) Combinatorial Theory. Springer-Verlag, New York.Google Scholar
Bailey, R. A., Praeger, C. E., Rowley, C. A. and Speed, T. P. (1983) Generalised wreath products of permutation groups. Proc. London Math. Soc. (3) 47, 69–82.Google Scholar
Hannan, E. J. (1965) Group representations and applied probability. J. Appl. Prob. 2, 1–68.CrossRefGoogle Scholar
James, A. T. (1957) The relationship algebra of an experimental design. Ann. Math. Statist. 28, 993–1002.Google Scholar
James, A. T. (1982) Analysis of variance determined by symmetry and combinatorial properties of zonal polynomials. In Statistics and Probability: Essays in Honor of C. R. Rao , ed. Kallianpur, G., Krishnaiah, P. R. and Ghosh, J. K., North-Holland, Amsterdam, 329–341.Google Scholar
Speed, T. P. and Bailey, R. A. (1982) On a class of association schemes derived from lattices of equivalence relations. In Algebraic Structures and Applications , ed. Schultz, P., Praeger, C. E. and Sullivan, R. P., Marcel Dekker, New York, 45–54.Google Scholar
Tukey, J. W. (1961) Discussion, emphasising the connection between analysis of variance and spectrum analysis. Technometrics 3, 1–29.Google Scholar