Classical Wishart distributions on the open convex cone of positive definite matrices and their fundamental features are extended to generalized Riesz and Wishart distributions associated with decomposable undirected graphs using the basic theory of exponential families. The families of these...

We consider normal [reverse not equivalent] Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of...

The first problem considered is that of testing for the reality of the covariance matrix of a p-dimensional complex normal distribution, while the second is that of testing that a 2p-dimensional real normal distribution has a p-dimensional complex structure. Both problems are reduced by...

A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product of conditional LFs, each factor having the form of a classical multivariate linear regression model...