On hypothesis tests for covariance matrices under multivariate normality

Abstract

In this paper we proposed a new statistical test for testing the covariance matrix in one population under multivariate normal assumption. In general, the proposed and the likelihood-ratio tests resulted in larger values of estimated powers than VMAX for bivariate and trivariate cases. VMAX was not sensitive to general changes in the covariance (correlation) structure. The advantage of the new test is that it is based on the comparison of all elements of the postulated covariance matrix under the null hypothesis with their respective maximum likelihood sample estimates and therefore, it does not restrict the information of the covariance matrix into a scalar number such as the determinant or trace, for example. Due to the fact that it is based on the maximum likelihood estimates and the Fisher information matrix, it can be used for data coming from distribution other than the multivariate normal.