# NONNULL DISTRIBUTION OF LRC FOR TESTING HOMOGENEITY OF COVARIANCE MATRICES OF COMPLETELY SYMMETRIC GAUSSIAN MODELS

## DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4563## Keywords:

Completely symmetric model, Nonnull moments, Zonal polynomials, Generalized hypergeometric function, Distribution## Abstract

The nonnull moments of the likelihood ratio statistic for testing equality of covariance matrices of completely symmetric Gaussian models are obta.ined in terms of the Lauricella's hypergeometric functions and also in terms of zonal polynomials. Then the nonnull asymptotic distribution of the statistic is derived under certain alternatives for unequal samples.

## References

Anderson, T. W. An Introduction to Multivariate Statistical Analysis, 2nd Edition. John Wiley, New York, (1984).

Gupta, A. K. Chattopadhyay, A. K. and Krishnaiah, P. R. "Asymptotic distribution of the determinant of some random matrices", Comm. Statist., 4, (1975) 33-47.

Gupta, A. K. and Nagar, D. K. "Testing equality of covariance matrices under intraclass correlation structure", Tamkang J. Math., 17(4), (1986) 7-16.

Gupta, A. K. and Nagar, D. K. "Nonnull distribution of the likelihood ratio criterion for testing equality of covariance matrices under intraclass correlation model", Comm. Statist. Theory - Meth. 16(1987), 3323-3341.

Gupta, A. K. and Na.gar, D. K. "Asymptotic expansion of the nonnull distribution of likelihood ratio statistic for testing multisample sphericity", Comm. Statist. Theory-Meth. 17, (1988a) 3145-3156.

Gupta, A. K. and Nagar, D. K. "Nonnull distribution of likelihood ratio criterion for testing multisample sphericity in the complex case", Aust. J. Statist. 30, (1988b) 307-318.

Han, C. P. "Testing the equality of covariance matrices under intraclass correlation models", Ann. Inst. Statist. Math., 27, (1975) 349-356.

James, A. T. "Distribution of matrix variates and latent roots deived from normal samples", Ann. Math. Statist., 35, (1964) 475-501.

Khatri, C. G. and Srivastava M. S. "Asymptotic expansions of the nonnull distributions of likelihood ratio criteria for covariance matrices" Ann. Statist., 2, (1974) 109-117.

Krishnaiah, P. R. and Pathak, P. K. "Tests for the equality of covariance matrices under the intraclass correlation model", Ann. Math. Statist., 38, (1967) 1286-1288.

Slater, L. J. Generalized Hypergeometric Functions. Cambridge University Press, London, (1966).

Tayal, Vipin, Gupta, A. K. and Nagar, D. K. "Testing homogeneity of covariances matrices of completely symmetric Gaussian models," Metron, 47, (1989), 334-346.

## Downloads

## Published

## How to Cite

*Tamkang Journal of Mathematics*,

*22*(1), 13–24. https://doi.org/10.5556/j.tkjm.22.1991.4563

## Issue

## Section

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.