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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

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    Chakravorti, S. (1968). On the analysis of variance test in multivariate variance components model,Calcutta Statist. Ass. Bull.,17, 57–78.MathSciNetCrossRefGoogle Scholar
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    James, A. T. (1964). Distributions of matrix variates and latent roots derived from normal samples,Ann. Math. Statist,35, 475–501.MathSciNetCrossRefGoogle Scholar
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    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.MathSciNetCrossRefGoogle Scholar
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    Roy, S. N. and Gnanadesikan, R. (1959). Some contributions to ANOVA in one or more dimensions: II,Ann. Math. Statist,30, 318–339.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1982

Authors and Affiliations

  • A. W. Davis

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