Some optima of parameter tests for an elliptically contoured distribution class (Q1109457)

An \(n\times p\) random matrix is said to have a third matrix elliptically contoured distribution if its characteristic function has the form \[ [\exp (i\sum^{n}_{j=1}t_ j\mu_ j)]\Phi (\sum^{n}_{j=1}t_ j'\Sigma_ jt_ j). \] The author shows that many likelihood ratio tests involving such distributions are uniformly most powerful or UMP invariant.