Abstract
Let S ∼ Wp (n, Σ), where Σ (p × p) is an unknown positive definite matrix. Let q (<p) be the number of variates on which additional information is available and Yi ∼ Nq (0, Σ11), i = 1, 2,…,m. We obtain minimax estimators of Σ and Σ−1. Monte Carlo simulation indicates that the minimax estimators have smaller risk than the maximum likelihood estimators for p = 2, q = 1 and p = 3, q = 1.