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...

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...

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...

In this paper, we define general canonical correlations, which generalize the canonical correlations developed by Hotelling, and general canonical covariate pairs, the corresponding linear statistic. We also define canonical variance distances with corresponding canonical distance variates. In a...

Jensen's inequality f(EX) = Ef(X) for the expectation of a convex function of a random variable is extended to a generalized class of convex functions f whose domain and range are subsets of (possibly) infinite-dimensional linear topological spaces. Convexity of f is defined with respect to...

Consider a generalized random variable X assuming values in a Banach space 4 with conjugate space 4*. For separable or reflexive 4 the measurability, probability distribution, and other properties of X are characterized in terms of a collection of real random variables {a*(X) : a* [set...

It is shown that for the MANOVA problem the power function of the test based on the trace of a multivariate beta matrix is monotonically increasing in each noncentrality parameter provided that the cutoff point is not too large. This result is also true for the problem of testing independence of...

Let V1,..., Vm, W1,..., Wn be independent p - 1 random vectors having multivariate normal distributions with common nonsingular covariance matrix [Sigma] and with EW[alpha] = 0, [alpha] = 1,..., n. In this canonical form of the multivariate linear model, the problem is to test H: EV[alpha] az...