Improved likelihood ratio statistics for covariance selection models

The expected value of the likelihood ratio statistic for covariance selection models, when this statistic has a closed form, is derived correct to terms of order n−2, n being the sample size. Then a Bartlett-type correction factor is available for such statistics. By simulation, the practical use of such a correction factor is illustrated, and is compared with an alternative correction factor in a special case. The null density of the corrected statistic is also considered.