Certain results of information theory are applied to some problems of multivariate analysis, including the multivariate linear hypothesis and the hypothesis of homogeneity of covariance matrices. A discussion of certain related linear discriminant functions is also included. Some asymptotic distributions on the null hypothesis are derived. Related problems, still under investigation, are mentioned. The procedures are based on the principle of maximizing information. For the cases considered, the estimates of $I(1:2)$ and $J(1,2)$ turn out to be those obtained by replacing the parameters by unbiased estimates, appropriate to the hypotheses under consideration.
S. Kullback. "An Application of Information Theory to Multivariate Analysis, II." Ann. Math. Statist. 27 (1) 122 - 146, March, 1956. https://doi.org/10.1214/aoms/1177728353