Testing the equality of several covariance matrices

Abstract

Using a new approach based on Meijer G-functions and computer simulation, we numerically compute the exact null distribution of the modified-likelihood ratio statistic used to test the hypothesis that several covariances matrices of normal distributions are equal. Small samples of different sizes are considered, and for the case of two matrices, we introduce a new test based on determinants, with the null distribution of its criterion also fully computable. Comparisons with published results show the accuracy of our approach, which is proved to be more flexible and adaptable to different cases.

Keywords:

• covariance matrix
• likelihood ratio
• beta distribution
• Meijer function
• latent roots
• determinant
• simulation
• percentiles

AMS Classification :

• 62H10
• 33A35

Acknowledgements

Research partially supported by NSERC Grant A 9249 (Canada). The authors wish to thank an anonymous referee for several helpful criticisms and suggestions that have led to our improved paper. Also thanks to Prof. A. Bennington for proofreading the entire paper and suggesting several style and presentation changes.