TESTS IN COVARIANCE-SELECTION MODELS

Consider the likelihood ratio test between two nested covariance selec tion models, It is shown that the distribution of the test statistic r aised to the power 2/n can be approximated by a product of independent beta distributions, Furthermore, conditions ensuring erectness of the approximation is given, and for this case the test statistic is shown to be independent of the maximum likelihood estimator under the null hypothesis, A simulation study reveals that the approximation is much superior to the usual chi-square approximation for small and moderate sample sizes.