Proportionality of covariance matrices of n independent p-dimensional normal distributions with the same type of linear restrictions of the inverse covariances is considered. Conditions for existence and uniqueness of the maximum likelihood estimator are obtained through the development of general results for scale-invariant natural exponential families.
"Estimation of proportional covariances in the presene of certain linear restrictions." Ann. Statist. 32 (1) 219 - 232, February 2004. https://doi.org/10.1214/aos/1079120134