Majorization, polyhedra, and statistical testing problems Original Research Article

There are important connections between majorization and convex polyhedra. Both weak majorization and majorization are preorders related to certain simple convex cones. We investigate the facial structure of a polyhedral cone C associated with a layered directed graph. A generalization of weak majorization based on C is introduced. It defines a preorder of matrices. An application in statistical testing theory is discussed in some detail.