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Three statistical tests for testing the covariance matrix in one population under multivariate normal assumption were developed and compared with the classical generalized variance test by means of Monte Carlo simulation. It is shown that the tests, which are based on the eigenvalues of the sample and the theoretical covariances matrices, presented better performance than the generalized variance particularly in cases which the parameters (determinant and traces) of the covariances matrices under the null and alternative hypothesis were similar. Since the three statistical tests are of simple implementation they can be considered as alternatives to be used in a general context.

Alternative Hypothesis Tests for the Covariance Matrix Based on Eigenvalues and Multivariate Normality