Performance evaluation of likelihood-ratio tests for assessing similarity of the covariance matrices of two multivariate normal populations

Abstract

In analyzing two multivariate normal data sets, the assumption about equality of covariance matrices is usually used as a default for doing subsequence inferences. If this equality doesn’t hold, later inferences will be more complex and usually approximate. If one detects some identical components between two decomposed non equal covariance matrices and uses this extra information, one expects that subsequence inferences can be more accurately performed. For this purpose, in this article we consider some statistical tests about the equality of components of decomposed covariance matrices of two multivariate normal populations. Our emphasis is on the spectral decomposition of these matrices. Hypotheses about the equalities of sizes, shapes, and set of directions as components of these two covariance matrices are tested by the likelihood ratio test (LRT). Some simulation studies are carried out to investigate the accuracy and power of the LRT. Finally, analyses of two real data sets are illustrated.