Testing equality of generalized variances of k multivariate normal populations

ABSTRACT

Generalized variance is a measure of dispersion of multivariate data. Comparison of dispersion of multivariate data is one of the favorite issues for multivariate quality control, generalized homogeneity of multidimensional scatter, etc. In this article, the problem of testing equality of generalized variances of k multivariate normal populations by using the Bartlett's modified likelihood ratio test (BMLRT) is proposed. Simulations to compare the Type I error rate and power of the BMLRT and the likelihood ratio test (LRT) methods are performed. These simulations show that the BMLRT method has a better chi-square approximation under the null hypothesis. Finally, a practical example is given.

KEYWORDS:

• Affine invariant
• Bartlett correction
• Generalized variance
• Likelihood ratio test
• Taylor expansion

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-XX
• 62H15