Abstract: Muirhead and Verathaworn (1985) and Konno (1991a,b) extended the Wishart identity to the multivariate F distribution and used this identity to prove dominance results for estimating the scale matrix of the multivariate F distribution. This paper extends this F identity to the noncentral multivariate F distribution. As an application of this noncentral F identity, we consider the problem of estimating the noncentrality matrix of a noncentral multivariate F distribution. This identity is used to develop a class of orthogonally invariant estimators which dominate the usual unbiased estimator. A simulation study was carried out to compare the performance of these estimators.
Key words and phrases: Wishart identity, noncentrality matrix, decision-theoretic estimation, noncentral multivariate F distribution.