Indiana University - Department of Mathematics
The General Wishart distribution will be introduced by means of a representation using generalized positive definite (psd) matrices in a Vinberg algebra. The following topics will be discussed:
1. The complete solution to several classical testing problems extended to generalized Wishart models.
2. The extension of several classical results concerning the convex cone of positive definite matrices and the standard Wishart distributions.
3. The special case where all entries of the generalized psd matrices are real valued.
4. The variance function of the general Wishart distributions.
5. The extensions of generalized Wishart models in (3) to the case of directed acyclic graphs.