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Annals of the Institute of Statistical Mathematics

, Volume 34, Issue 3, pp 517–521

# On a result of roy and Gnanadesikan concerning multivariete variance components

• A. W. Davis
Article

## Summary

Roy and Gnanadesikan [5] showed that inference for a general multivariate variance components model may be carried out using the standard multivariateF distribution under certain condtions. It is shown in this note that the theory of zonal polynomials, and their extension by the author to invariant polynomials in two matrix arguments, provide a concise approach to the derivation of these conditions. Relevant distributions are also derived for the general case.

## Keywords

Latent Root Invariant Polynomial Wishart Distribution Matrix Argument Zonal Polynomial

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## References

1. [1]
Chakravorti, S. (1968). On the analysis of variance test in multivariate variance components model,Calcutta Statist. Ass. Bull.,17, 57–78.
2. [2]
Davis, A. W. (1979). Invariant polynomials with two matrix arguments extending the zonal polynomials: applications to multivariate distribution theory,Ann. Inst. Statist. Math.,31, A, 465–485.
3. [3]
James, A. T. (1964). Distributions of matrix variates and latent roots derived from normal samples,Ann. Math. Statist,35, 475–501.
4. [4]
Roy, S. N. and Cobb, W. (1960). Mixed model variance analysis with normal error and possibly non-normal other random effects, I. The univariate case, II. The multivariate case,Ann. Math. Statist.,31, 939–957, 958–968.
5. [5]
Roy, S. N. and Gnanadesikan, R. (1959). Some contributions to ANOVA in one or more dimensions: II,Ann. Math. Statist,30, 318–339.

## Copyright information

© The Institute of Statistical Mathematics, Tokyo 1982

## Authors and Affiliations

• A. W. Davis

There are no affiliations available